exp_final_two – Complete Experiment Report
Vary_Correlation_with_high_Dimension
(MvNormal,
correlation,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-7.369 |
1.17e-09 |
-1.660 |
| HMC |
0.3 |
1.754 |
0.0868 |
0.751 |
| HMC |
0.5 |
2.865 |
0.00672 |
1.383 |
| HMC |
0.9 |
4.598 |
6.68e-05 |
4.358 |
| HMC |
0.95 |
5.080 |
1.66e-05 |
4.675 |
| HMC |
0.99 |
4.735 |
4.88e-05 |
6.357 |
| SMC |
0.0 |
-0.990 |
0.327 |
-0.218 |
| SMC |
0.3 |
0.195 |
0.846 |
0.046 |
| SMC |
0.5 |
1.211 |
0.231 |
0.295 |
| SMC |
0.9 |
-0.326 |
0.746 |
-0.078 |
| SMC |
0.95 |
-0.002 |
0.998 |
-0.001 |
| SMC |
0.99 |
0.256 |
0.799 |
0.070 |
| Metro |
0.0 |
13.671 |
2.77e-18 |
4.711 |
| Metro |
0.3 |
6.518 |
2.79e-07 |
6.349 |
| Metro |
0.5 |
7.452 |
2.82e-08 |
12.659 |
| Metro |
0.9 |
6.108 |
1.17e-06 |
24.672 |
| Metro |
0.95 |
6.436 |
4.81e-07 |
37.101 |
| Metro |
0.99 |
7.139 |
7.37e-08 |
57.648 |
| DEMetro_Z |
0.0 |
46.026 |
1.15e-28 |
2226.429 |
| DEMetro_Z |
0.3 |
33.614 |
8.86e-25 |
1158.391 |
| DEMetro_Z |
0.5 |
47.380 |
4.98e-29 |
878.882 |
| DEMetro_Z |
0.9 |
49.351 |
1.51e-29 |
490.360 |
| DEMetro_Z |
0.95 |
47.348 |
4.99e-29 |
528.340 |
| DEMetro_Z |
0.99 |
35.011 |
2.75e-25 |
438.494 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-46.074
|
1.12e-28
|
-8.412
|
| HMC_vs_DEMetro_Z |
0.3
|
-33.651
|
8.6e-25
|
-6.144
|
| HMC_vs_DEMetro_Z |
0.5
|
-47.168
|
5.72e-29
|
-8.612
|
| HMC_vs_DEMetro_Z |
0.9
|
-49.358
|
1.56e-29
|
-9.012
|
| HMC_vs_DEMetro_Z |
0.95
|
-46.986
|
6.39e-29
|
-8.578
|
| HMC_vs_DEMetro_Z |
0.99
|
-34.862
|
3.16e-25
|
-6.365
|
| Metro_vs_SMC |
0.0
|
15.586
|
1.24e-15
|
2.846
|
| Metro_vs_SMC |
0.3
|
6.514
|
3.93e-07
|
1.189
|
| Metro_vs_SMC |
0.5
|
7.052
|
9.31e-08
|
1.288
|
| Metro_vs_SMC |
0.9
|
6.218
|
8.77e-07
|
1.135
|
| Metro_vs_SMC |
0.95
|
6.450
|
4.67e-07
|
1.178
|
| Metro_vs_SMC |
0.99
|
7.132
|
7.54e-08
|
1.302
|
| Metro_vs_DEMetro_Z |
0.0
|
-45.976
|
1.19e-28
|
-8.394
|
| Metro_vs_DEMetro_Z |
0.3
|
-33.427
|
1.04e-24
|
-6.103
|
| Metro_vs_DEMetro_Z |
0.5
|
-47.737
|
4.05e-29
|
-8.716
|
| Metro_vs_DEMetro_Z |
0.9
|
-43.487
|
5.84e-28
|
-7.940
|
| Metro_vs_DEMetro_Z |
0.95
|
-44.215
|
3.64e-28
|
-8.072
|
| Metro_vs_DEMetro_Z |
0.99
|
-31.528
|
5.43e-24
|
-5.756
|
| HMC_vs_Metro |
0.0
|
-21.750
|
1.67e-19
|
-3.971
|
| HMC_vs_Metro |
0.3
|
-5.097
|
1.94e-05
|
-0.931
|
| HMC_vs_Metro |
0.5
|
-6.374
|
5.75e-07
|
-1.164
|
| HMC_vs_Metro |
0.9
|
-5.026
|
2.36e-05
|
-0.918
|
| HMC_vs_Metro |
0.95
|
-5.839
|
2.48e-06
|
-1.066
|
| HMC_vs_Metro |
0.99
|
-6.375
|
5.73e-07
|
-1.164
|
| HMC_vs_SMC |
0.0
|
-9.114
|
5.19e-10
|
-1.664
|
| HMC_vs_SMC |
0.3
|
1.795
|
0.0831
|
0.328
|
| HMC_vs_SMC |
0.5
|
2.356
|
0.0255
|
0.430
|
| HMC_vs_SMC |
0.9
|
4.652
|
6.66e-05
|
0.849
|
| HMC_vs_SMC |
0.95
|
4.873
|
3.62e-05
|
0.890
|
| HMC_vs_SMC |
0.99
|
4.547
|
8.92e-05
|
0.830
|
| DEMetro_Z_vs_SMC |
0.0
|
46.048
|
1.14e-28
|
8.407
|
| DEMetro_Z_vs_SMC |
0.3
|
33.633
|
8.73e-25
|
6.141
|
| DEMetro_Z_vs_SMC |
0.5
|
47.301
|
5.27e-29
|
8.636
|
| DEMetro_Z_vs_SMC |
0.9
|
49.180
|
1.73e-29
|
8.979
|
| DEMetro_Z_vs_SMC |
0.95
|
47.162
|
5.74e-29
|
8.611
|
| DEMetro_Z_vs_SMC |
0.99
|
34.959
|
2.92e-25
|
6.383
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.018 |
0.023 |
0.003 |
-1.660 |
| HMC |
0.3 |
0.027 |
0.023 |
0.006 |
0.751 |
| HMC |
0.5 |
0.031 |
0.021 |
0.008 |
1.383 |
| HMC |
0.9 |
0.078 |
0.019 |
0.013 |
4.358 |
| HMC |
0.95 |
0.076 |
0.020 |
0.012 |
4.675 |
| HMC |
0.99 |
0.110 |
0.019 |
0.014 |
6.357 |
| SMC |
0.0 |
0.022 |
0.023 |
0.003 |
-0.218 |
| SMC |
0.3 |
0.023 |
0.023 |
0.006 |
0.046 |
| SMC |
0.5 |
0.023 |
0.021 |
0.008 |
0.295 |
| SMC |
0.9 |
0.018 |
0.019 |
0.013 |
-0.078 |
| SMC |
0.95 |
0.020 |
0.020 |
0.012 |
-0.001 |
| SMC |
0.99 |
0.020 |
0.019 |
0.014 |
0.070 |
| Metro |
0.0 |
0.037 |
0.023 |
0.003 |
4.711 |
| Metro |
0.3 |
0.061 |
0.023 |
0.006 |
6.349 |
| Metro |
0.5 |
0.117 |
0.021 |
0.008 |
12.659 |
| Metro |
0.9 |
0.350 |
0.019 |
0.013 |
24.672 |
| Metro |
0.95 |
0.466 |
0.020 |
0.012 |
37.101 |
| Metro |
0.99 |
0.847 |
0.019 |
0.014 |
57.648 |
| DEMetro_Z |
0.0 |
6.576 |
0.023 |
0.003 |
2226.429 |
| DEMetro_Z |
0.3 |
6.941 |
0.023 |
0.006 |
1158.391 |
| DEMetro_Z |
0.5 |
6.672 |
0.021 |
0.008 |
878.882 |
| DEMetro_Z |
0.9 |
6.595 |
0.019 |
0.013 |
490.360 |
| DEMetro_Z |
0.95 |
6.374 |
0.020 |
0.012 |
528.340 |
| DEMetro_Z |
0.99 |
6.314 |
0.019 |
0.014 |
438.494 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
10.620 |
1.37e-14 |
3.406 |
| HMC |
0.3 |
6.242 |
9.36e-08 |
2.094 |
| HMC |
0.5 |
3.818 |
0.0004 |
1.401 |
| HMC |
0.9 |
5.564 |
4.93e-06 |
9.708 |
| HMC |
0.95 |
4.865 |
3.08e-05 |
4.462 |
| HMC |
0.99 |
5.080 |
1.79e-05 |
5.996 |
| SMC |
0.0 |
3.975 |
0.0002 |
1.097 |
| SMC |
0.3 |
2.121 |
0.0386 |
0.666 |
| SMC |
0.5 |
2.935 |
0.00508 |
1.013 |
| SMC |
0.9 |
2.191 |
0.0329 |
0.671 |
| SMC |
0.95 |
-2.311 |
0.0244 |
-0.584 |
| SMC |
0.99 |
0.322 |
0.749 |
0.080 |
| Metro |
0.0 |
14.655 |
2e-18 |
5.828 |
| Metro |
0.3 |
10.908 |
1.24e-12 |
7.100 |
| Metro |
0.5 |
7.803 |
1.1e-08 |
12.348 |
| Metro |
0.9 |
7.950 |
8.79e-09 |
29.149 |
| Metro |
0.95 |
6.115 |
1.16e-06 |
46.570 |
| Metro |
0.99 |
5.085 |
2e-05 |
82.884 |
| DEMetro_Z |
0.0 |
37.314 |
4.59e-26 |
48653.099 |
| DEMetro_Z |
0.3 |
31.375 |
6.22e-24 |
40102.407 |
| DEMetro_Z |
0.5 |
38.648 |
1.69e-26 |
34942.664 |
| DEMetro_Z |
0.9 |
40.390 |
4.81e-27 |
19605.728 |
| DEMetro_Z |
0.95 |
43.401 |
6.18e-28 |
9803.004 |
| DEMetro_Z |
0.99 |
33.324 |
1.13e-24 |
6898.138 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
6.884
|
1.46e-07
|
1.257
|
| HMC_vs_SMC |
0.3
|
3.828
|
0.000637
|
0.699
|
| HMC_vs_SMC |
0.5
|
0.782
|
0.441
|
0.143
|
| HMC_vs_SMC |
0.9
|
5.174
|
1.57e-05
|
0.945
|
| HMC_vs_SMC |
0.95
|
5.711
|
3.53e-06
|
1.043
|
| HMC_vs_SMC |
0.99
|
5.149
|
1.67e-05
|
0.940
|
| Metro_vs_DEMetro_Z |
0.0
|
-37.309
|
4.61e-26
|
-6.812
|
| Metro_vs_DEMetro_Z |
0.3
|
-31.370
|
6.25e-24
|
-5.727
|
| Metro_vs_DEMetro_Z |
0.5
|
-38.638
|
1.7e-26
|
-7.054
|
| Metro_vs_DEMetro_Z |
0.9
|
-40.299
|
5.13e-27
|
-7.358
|
| Metro_vs_DEMetro_Z |
0.95
|
-43.085
|
7.62e-28
|
-7.866
|
| Metro_vs_DEMetro_Z |
0.99
|
-32.105
|
3.25e-24
|
-5.862
|
| HMC_vs_Metro |
0.0
|
-6.018
|
1.52e-06
|
-1.099
|
| HMC_vs_Metro |
0.3
|
-7.690
|
1.77e-08
|
-1.404
|
| HMC_vs_Metro |
0.5
|
-6.791
|
1.87e-07
|
-1.240
|
| HMC_vs_Metro |
0.9
|
-4.416
|
0.000128
|
-0.806
|
| HMC_vs_Metro |
0.95
|
-5.623
|
4.5e-06
|
-1.027
|
| HMC_vs_Metro |
0.99
|
-4.628
|
7.13e-05
|
-0.845
|
| HMC_vs_DEMetro_Z |
0.0
|
-37.312
|
4.6e-26
|
-6.812
|
| HMC_vs_DEMetro_Z |
0.3
|
-31.373
|
6.23e-24
|
-5.728
|
| HMC_vs_DEMetro_Z |
0.5
|
-38.642
|
1.7e-26
|
-7.055
|
| HMC_vs_DEMetro_Z |
0.9
|
-40.387
|
4.82e-27
|
-7.374
|
| HMC_vs_DEMetro_Z |
0.95
|
-43.374
|
6.29e-28
|
-7.919
|
| HMC_vs_DEMetro_Z |
0.99
|
-33.315
|
1.14e-24
|
-6.082
|
| Metro_vs_SMC |
0.0
|
11.372
|
3.31e-12
|
2.076
|
| Metro_vs_SMC |
0.3
|
10.097
|
5.3e-11
|
1.843
|
| Metro_vs_SMC |
0.5
|
7.039
|
9.65e-08
|
1.285
|
| Metro_vs_SMC |
0.9
|
7.878
|
1.09e-08
|
1.438
|
| Metro_vs_SMC |
0.95
|
6.219
|
8.75e-07
|
1.135
|
| Metro_vs_SMC |
0.99
|
5.085
|
2.01e-05
|
0.928
|
| DEMetro_Z_vs_SMC |
0.0
|
37.315
|
4.59e-26
|
6.813
|
| DEMetro_Z_vs_SMC |
0.3
|
31.375
|
6.22e-24
|
5.728
|
| DEMetro_Z_vs_SMC |
0.5
|
38.646
|
1.69e-26
|
7.056
|
| DEMetro_Z_vs_SMC |
0.9
|
40.388
|
4.82e-27
|
7.374
|
| DEMetro_Z_vs_SMC |
0.95
|
43.398
|
6.19e-28
|
7.923
|
| DEMetro_Z_vs_SMC |
0.99
|
33.323
|
1.14e-24
|
6.084
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.044 |
0.032 |
0.004 |
3.406 |
| HMC |
0.3 |
0.040 |
0.031 |
0.004 |
2.094 |
| HMC |
0.5 |
0.037 |
0.030 |
0.005 |
1.401 |
| HMC |
0.9 |
0.114 |
0.024 |
0.009 |
9.708 |
| HMC |
0.95 |
0.110 |
0.035 |
0.017 |
4.462 |
| HMC |
0.99 |
0.161 |
0.031 |
0.022 |
5.996 |
| SMC |
0.0 |
0.035 |
0.032 |
0.004 |
1.097 |
| SMC |
0.3 |
0.034 |
0.031 |
0.004 |
0.666 |
| SMC |
0.5 |
0.035 |
0.030 |
0.005 |
1.013 |
| SMC |
0.9 |
0.030 |
0.024 |
0.009 |
0.671 |
| SMC |
0.95 |
0.025 |
0.035 |
0.017 |
-0.584 |
| SMC |
0.99 |
0.033 |
0.031 |
0.022 |
0.080 |
| Metro |
0.0 |
0.052 |
0.032 |
0.004 |
5.828 |
| Metro |
0.3 |
0.062 |
0.031 |
0.004 |
7.100 |
| Metro |
0.5 |
0.095 |
0.030 |
0.005 |
12.348 |
| Metro |
0.9 |
0.294 |
0.024 |
0.009 |
29.149 |
| Metro |
0.95 |
0.826 |
0.035 |
0.017 |
46.570 |
| Metro |
0.99 |
1.818 |
0.031 |
0.022 |
82.884 |
| DEMetro_Z |
0.0 |
172.552 |
0.032 |
0.004 |
48653.099 |
| DEMetro_Z |
0.3 |
173.314 |
0.031 |
0.004 |
40102.407 |
| DEMetro_Z |
0.5 |
183.257 |
0.030 |
0.005 |
34942.664 |
| DEMetro_Z |
0.9 |
181.976 |
0.024 |
0.009 |
19605.728 |
| DEMetro_Z |
0.95 |
166.644 |
0.035 |
0.017 |
9803.004 |
| DEMetro_Z |
0.99 |
148.704 |
0.031 |
0.022 |
6898.138 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.243 |
0.0293 |
-0.493 |
| HMC |
0.3 |
2.788 |
0.00807 |
1.257 |
| HMC |
0.5 |
3.807 |
0.000514 |
1.983 |
| HMC |
0.9 |
6.888 |
1.12e-07 |
8.147 |
| HMC |
0.95 |
7.657 |
1.21e-08 |
7.463 |
| HMC |
0.99 |
7.836 |
1.02e-08 |
12.910 |
| SMC |
0.0 |
-0.319 |
0.751 |
-0.074 |
| SMC |
0.3 |
0.844 |
0.402 |
0.199 |
| SMC |
0.5 |
1.902 |
0.0624 |
0.446 |
| SMC |
0.9 |
0.022 |
0.983 |
0.005 |
| SMC |
0.95 |
-0.730 |
0.468 |
-0.179 |
| SMC |
0.99 |
0.553 |
0.582 |
0.156 |
| Metro |
0.0 |
16.267 |
7.65e-21 |
5.908 |
| Metro |
0.3 |
7.104 |
6.37e-08 |
8.852 |
| Metro |
0.5 |
8.318 |
3.2e-09 |
17.506 |
| Metro |
0.9 |
7.861 |
1.12e-08 |
40.384 |
| Metro |
0.95 |
10.272 |
3.5e-11 |
62.374 |
| Metro |
0.99 |
10.820 |
1.06e-11 |
111.561 |
| DEMetro_Z |
0.0 |
68.464 |
1.27e-33 |
6006.686 |
| DEMetro_Z |
0.3 |
66.806 |
2.58e-33 |
3123.408 |
| DEMetro_Z |
0.5 |
82.888 |
5.1e-36 |
2450.645 |
| DEMetro_Z |
0.9 |
95.546 |
8.26e-38 |
1423.052 |
| DEMetro_Z |
0.95 |
102.759 |
1e-38 |
1366.570 |
| DEMetro_Z |
0.99 |
63.071 |
1.34e-32 |
1234.892 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-68.439
|
1.29e-33
|
-12.495
|
| Metro_vs_DEMetro_Z |
0.3
|
-66.497
|
2.96e-33
|
-12.141
|
| Metro_vs_DEMetro_Z |
0.5
|
-82.494
|
5.88e-36
|
-15.061
|
| Metro_vs_DEMetro_Z |
0.9
|
-87.275
|
1.16e-36
|
-15.934
|
| Metro_vs_DEMetro_Z |
0.95
|
-84.548
|
2.89e-36
|
-15.436
|
| Metro_vs_DEMetro_Z |
0.99
|
-48.540
|
2.51e-29
|
-8.862
|
| DEMetro_Z_vs_SMC |
0.0
|
68.497
|
1.26e-33
|
12.506
|
| DEMetro_Z_vs_SMC |
0.3
|
66.811
|
2.58e-33
|
12.198
|
| DEMetro_Z_vs_SMC |
0.5
|
82.857
|
5.18e-36
|
15.128
|
| DEMetro_Z_vs_SMC |
0.9
|
95.461
|
8.66e-38
|
17.429
|
| DEMetro_Z_vs_SMC |
0.95
|
102.510
|
1.1e-38
|
18.716
|
| DEMetro_Z_vs_SMC |
0.99
|
63.229
|
1.26e-32
|
11.544
|
| HMC_vs_DEMetro_Z |
0.0
|
-68.479
|
1.27e-33
|
-12.502
|
| HMC_vs_DEMetro_Z |
0.3
|
-66.940
|
2.44e-33
|
-12.222
|
| HMC_vs_DEMetro_Z |
0.5
|
-82.770
|
5.34e-36
|
-15.112
|
| HMC_vs_DEMetro_Z |
0.9
|
-94.464
|
1.17e-37
|
-17.247
|
| HMC_vs_DEMetro_Z |
0.95
|
-101.743
|
1.37e-38
|
-18.576
|
| HMC_vs_DEMetro_Z |
0.99
|
-62.974
|
1.42e-32
|
-11.497
|
| HMC_vs_Metro |
0.0
|
-20.735
|
6.16e-19
|
-3.786
|
| HMC_vs_Metro |
0.3
|
-5.540
|
5.66e-06
|
-1.012
|
| HMC_vs_Metro |
0.5
|
-7.118
|
7.83e-08
|
-1.300
|
| HMC_vs_Metro |
0.9
|
-6.258
|
7.87e-07
|
-1.143
|
| HMC_vs_Metro |
0.95
|
-9.279
|
3.51e-10
|
-1.694
|
| HMC_vs_Metro |
0.99
|
-9.614
|
1.6e-10
|
-1.755
|
| HMC_vs_SMC |
0.0
|
-2.694
|
0.0116
|
-0.492
|
| HMC_vs_SMC |
0.3
|
2.692
|
0.0117
|
0.491
|
| HMC_vs_SMC |
0.5
|
3.080
|
0.0045
|
0.562
|
| HMC_vs_SMC |
0.9
|
6.672
|
2.56e-07
|
1.218
|
| HMC_vs_SMC |
0.95
|
7.583
|
2.33e-08
|
1.384
|
| HMC_vs_SMC |
0.99
|
7.728
|
1.6e-08
|
1.411
|
| Metro_vs_SMC |
0.0
|
17.126
|
1.05e-16
|
3.127
|
| Metro_vs_SMC |
0.3
|
6.994
|
1.09e-07
|
1.277
|
| Metro_vs_SMC |
0.5
|
7.974
|
8.56e-09
|
1.456
|
| Metro_vs_SMC |
0.9
|
7.969
|
8.67e-09
|
1.455
|
| Metro_vs_SMC |
0.95
|
10.391
|
2.74e-11
|
1.897
|
| Metro_vs_SMC |
0.99
|
10.806
|
1.11e-11
|
1.973
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.028 |
0.029 |
0.002 |
-0.493 |
| HMC |
0.3 |
0.033 |
0.029 |
0.003 |
1.257 |
| HMC |
0.5 |
0.036 |
0.027 |
0.004 |
1.983 |
| HMC |
0.9 |
0.085 |
0.024 |
0.007 |
8.147 |
| HMC |
0.95 |
0.081 |
0.025 |
0.007 |
7.463 |
| HMC |
0.99 |
0.125 |
0.024 |
0.008 |
12.910 |
| SMC |
0.0 |
0.029 |
0.029 |
0.002 |
-0.074 |
| SMC |
0.3 |
0.029 |
0.029 |
0.003 |
0.199 |
| SMC |
0.5 |
0.029 |
0.027 |
0.004 |
0.446 |
| SMC |
0.9 |
0.024 |
0.024 |
0.007 |
0.005 |
| SMC |
0.95 |
0.024 |
0.025 |
0.007 |
-0.179 |
| SMC |
0.99 |
0.026 |
0.024 |
0.008 |
0.156 |
| Metro |
0.0 |
0.039 |
0.029 |
0.002 |
5.908 |
| Metro |
0.3 |
0.058 |
0.029 |
0.003 |
8.852 |
| Metro |
0.5 |
0.103 |
0.027 |
0.004 |
17.506 |
| Metro |
0.9 |
0.324 |
0.024 |
0.007 |
40.384 |
| Metro |
0.95 |
0.489 |
0.025 |
0.007 |
62.374 |
| Metro |
0.99 |
0.895 |
0.024 |
0.008 |
111.561 |
| DEMetro_Z |
0.0 |
10.319 |
0.029 |
0.002 |
6006.686 |
| DEMetro_Z |
0.3 |
10.414 |
0.029 |
0.003 |
3123.408 |
| DEMetro_Z |
0.5 |
10.599 |
0.027 |
0.004 |
2450.645 |
| DEMetro_Z |
0.9 |
10.585 |
0.024 |
0.007 |
1423.052 |
| DEMetro_Z |
0.95 |
10.185 |
0.025 |
0.007 |
1366.570 |
| DEMetro_Z |
0.99 |
9.665 |
0.024 |
0.008 |
1234.892 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-3.311 |
0.0018 |
-0.698 |
| HMC |
0.3 |
2.644 |
0.0117 |
1.226 |
| HMC |
0.5 |
3.833 |
0.000478 |
2.024 |
| HMC |
0.9 |
7.985 |
5.56e-09 |
8.733 |
| HMC |
0.95 |
9.274 |
1.14e-10 |
6.939 |
| HMC |
0.99 |
7.750 |
1.13e-08 |
9.691 |
| SMC |
0.0 |
0.520 |
0.605 |
0.116 |
| SMC |
0.3 |
0.731 |
0.468 |
0.171 |
| SMC |
0.5 |
2.630 |
0.0109 |
0.681 |
| SMC |
0.9 |
0.354 |
0.725 |
0.088 |
| SMC |
0.95 |
-1.085 |
0.282 |
-0.258 |
| SMC |
0.99 |
0.317 |
0.752 |
0.084 |
| Metro |
0.0 |
14.385 |
6.1e-20 |
4.462 |
| Metro |
0.3 |
8.134 |
3.65e-09 |
8.565 |
| Metro |
0.5 |
9.203 |
3.58e-10 |
18.251 |
| Metro |
0.9 |
9.087 |
5.37e-10 |
40.878 |
| Metro |
0.95 |
13.104 |
9.8e-14 |
56.464 |
| Metro |
0.99 |
13.453 |
5.11e-14 |
63.382 |
| DEMetro_Z |
0.0 |
79.554 |
1.31e-35 |
332.840 |
| DEMetro_Z |
0.3 |
74.843 |
6.28e-35 |
230.100 |
| DEMetro_Z |
0.5 |
117.631 |
3.58e-41 |
200.432 |
| DEMetro_Z |
0.9 |
107.474 |
4.54e-41 |
117.901 |
| DEMetro_Z |
0.95 |
76.826 |
4.25e-36 |
102.910 |
| DEMetro_Z |
0.99 |
86.147 |
2.3e-38 |
88.580 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
79.145
|
1.95e-35
|
14.450
|
| DEMetro_Z_vs_SMC |
0.3
|
75.388
|
7.93e-35
|
13.764
|
| DEMetro_Z_vs_SMC |
0.5
|
114.299
|
4.73e-40
|
20.868
|
| DEMetro_Z_vs_SMC |
0.9
|
107.595
|
2.72e-39
|
19.644
|
| DEMetro_Z_vs_SMC |
0.95
|
76.657
|
4.9e-35
|
13.996
|
| DEMetro_Z_vs_SMC |
0.99
|
86.922
|
1.3e-36
|
15.870
|
| HMC_vs_Metro |
0.0
|
-20.927
|
4.79e-19
|
-3.821
|
| HMC_vs_Metro |
0.3
|
-6.045
|
1.41e-06
|
-1.104
|
| HMC_vs_Metro |
0.5
|
-7.921
|
9.78e-09
|
-1.446
|
| HMC_vs_Metro |
0.9
|
-7.117
|
7.85e-08
|
-1.299
|
| HMC_vs_Metro |
0.95
|
-11.544
|
2.31e-12
|
-2.108
|
| HMC_vs_Metro |
0.99
|
-11.651
|
1.85e-12
|
-2.127
|
| Metro_vs_DEMetro_Z |
0.0
|
-78.332
|
2.62e-35
|
-14.301
|
| Metro_vs_DEMetro_Z |
0.3
|
-66.519
|
2.93e-33
|
-12.145
|
| Metro_vs_DEMetro_Z |
0.5
|
-71.438
|
3.74e-34
|
-13.043
|
| Metro_vs_DEMetro_Z |
0.9
|
-17.030
|
1.22e-16
|
-3.109
|
| Metro_vs_DEMetro_Z |
0.95
|
-10.758
|
1.23e-11
|
-1.964
|
| Metro_vs_DEMetro_Z |
0.99
|
-5.307
|
1.08e-05
|
-0.969
|
| HMC_vs_SMC |
0.0
|
-4.530
|
9.36e-05
|
-0.827
|
| HMC_vs_SMC |
0.3
|
2.611
|
0.0141
|
0.477
|
| HMC_vs_SMC |
0.5
|
2.577
|
0.0153
|
0.470
|
| HMC_vs_SMC |
0.9
|
7.669
|
1.87e-08
|
1.400
|
| HMC_vs_SMC |
0.95
|
9.491
|
2.13e-10
|
1.733
|
| HMC_vs_SMC |
0.99
|
7.702
|
1.71e-08
|
1.406
|
| Metro_vs_SMC |
0.0
|
15.126
|
2.7e-15
|
2.762
|
| Metro_vs_SMC |
0.3
|
8.029
|
7.45e-09
|
1.466
|
| Metro_vs_SMC |
0.5
|
8.850
|
9.77e-10
|
1.616
|
| Metro_vs_SMC |
0.9
|
9.191
|
4.32e-10
|
1.678
|
| Metro_vs_SMC |
0.95
|
13.347
|
6.55e-14
|
2.437
|
| Metro_vs_SMC |
0.99
|
13.507
|
4.86e-14
|
2.466
|
| HMC_vs_DEMetro_Z |
0.0
|
-79.370
|
1.79e-35
|
-14.491
|
| HMC_vs_DEMetro_Z |
0.3
|
-73.321
|
1.77e-34
|
-13.386
|
| HMC_vs_DEMetro_Z |
0.5
|
-106.914
|
3.27e-39
|
-19.520
|
| HMC_vs_DEMetro_Z |
0.9
|
-72.689
|
2.27e-34
|
-13.271
|
| HMC_vs_DEMetro_Z |
0.95
|
-59.078
|
8.91e-32
|
-10.786
|
| HMC_vs_DEMetro_Z |
0.99
|
-58.006
|
1.51e-31
|
-10.590
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.013 |
0.014 |
0.002 |
-0.698 |
| HMC |
0.3 |
0.018 |
0.015 |
0.002 |
1.226 |
| HMC |
0.5 |
0.020 |
0.014 |
0.003 |
2.024 |
| HMC |
0.9 |
0.055 |
0.014 |
0.005 |
8.733 |
| HMC |
0.95 |
0.052 |
0.015 |
0.005 |
6.939 |
| HMC |
0.99 |
0.076 |
0.014 |
0.006 |
9.691 |
| SMC |
0.0 |
0.015 |
0.014 |
0.002 |
0.116 |
| SMC |
0.3 |
0.015 |
0.015 |
0.002 |
0.171 |
| SMC |
0.5 |
0.016 |
0.014 |
0.003 |
0.681 |
| SMC |
0.9 |
0.014 |
0.014 |
0.005 |
0.088 |
| SMC |
0.95 |
0.013 |
0.015 |
0.005 |
-0.258 |
| SMC |
0.99 |
0.015 |
0.014 |
0.006 |
0.084 |
| Metro |
0.0 |
0.022 |
0.014 |
0.002 |
4.462 |
| Metro |
0.3 |
0.036 |
0.015 |
0.002 |
8.565 |
| Metro |
0.5 |
0.065 |
0.014 |
0.003 |
18.251 |
| Metro |
0.9 |
0.209 |
0.014 |
0.005 |
40.878 |
| Metro |
0.95 |
0.320 |
0.015 |
0.005 |
56.464 |
| Metro |
0.99 |
0.416 |
0.014 |
0.006 |
63.382 |
| DEMetro_Z |
0.0 |
0.580 |
0.014 |
0.002 |
332.840 |
| DEMetro_Z |
0.3 |
0.585 |
0.015 |
0.002 |
230.100 |
| DEMetro_Z |
0.5 |
0.573 |
0.014 |
0.003 |
200.432 |
| DEMetro_Z |
0.9 |
0.576 |
0.014 |
0.005 |
117.901 |
| DEMetro_Z |
0.95 |
0.571 |
0.015 |
0.005 |
102.910 |
| DEMetro_Z |
0.99 |
0.576 |
0.014 |
0.006 |
88.580 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-6.417 |
2.98e-08 |
-1.551 |
| HMC |
0.3 |
2.029 |
0.0484 |
0.767 |
| HMC |
0.5 |
5.121 |
7.24e-06 |
2.151 |
| HMC |
0.9 |
4.049 |
0.000315 |
3.806 |
| HMC |
0.95 |
5.937 |
1.49e-06 |
6.118 |
| HMC |
0.99 |
5.237 |
1.19e-05 |
7.371 |
| SMC |
0.0 |
-1.153 |
0.254 |
-0.288 |
| SMC |
0.3 |
-0.233 |
0.816 |
-0.062 |
| SMC |
0.5 |
2.022 |
0.0485 |
0.654 |
| SMC |
0.9 |
1.039 |
0.303 |
0.285 |
| SMC |
0.95 |
0.317 |
0.752 |
0.087 |
| SMC |
0.99 |
-1.030 |
0.307 |
-0.250 |
| Metro |
0.0 |
13.995 |
7.35e-19 |
4.705 |
| Metro |
0.3 |
7.268 |
4.27e-08 |
9.981 |
| Metro |
0.5 |
7.327 |
3.93e-08 |
12.434 |
| Metro |
0.9 |
6.108 |
1.17e-06 |
25.587 |
| Metro |
0.95 |
7.803 |
1.31e-08 |
69.684 |
| Metro |
0.99 |
6.469 |
4.43e-07 |
86.237 |
| DEMetro_Z |
0.0 |
26.418 |
7.74e-22 |
3876.685 |
| DEMetro_Z |
0.3 |
28.650 |
8.01e-23 |
2005.937 |
| DEMetro_Z |
0.5 |
35.936 |
1.33e-25 |
1538.703 |
| DEMetro_Z |
0.9 |
46.667 |
7.69e-29 |
873.192 |
| DEMetro_Z |
0.95 |
36.580 |
8.03e-26 |
857.782 |
| DEMetro_Z |
0.99 |
29.061 |
5.35e-23 |
719.048 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-26.423
|
7.7e-22
|
-4.824
|
| HMC_vs_DEMetro_Z |
0.3
|
-28.688
|
7.72e-23
|
-5.238
|
| HMC_vs_DEMetro_Z |
0.5
|
-35.861
|
1.42e-25
|
-6.547
|
| HMC_vs_DEMetro_Z |
0.9
|
-47.014
|
6.28e-29
|
-8.583
|
| HMC_vs_DEMetro_Z |
0.95
|
-36.439
|
9.01e-26
|
-6.653
|
| HMC_vs_DEMetro_Z |
0.99
|
-28.539
|
8.93e-23
|
-5.210
|
| Metro_vs_SMC |
0.0
|
14.850
|
4.35e-15
|
2.711
|
| Metro_vs_SMC |
0.3
|
7.047
|
9.45e-08
|
1.287
|
| Metro_vs_SMC |
0.5
|
7.343
|
4.34e-08
|
1.341
|
| Metro_vs_SMC |
0.9
|
6.006
|
1.57e-06
|
1.096
|
| Metro_vs_SMC |
0.95
|
7.792
|
1.36e-08
|
1.423
|
| Metro_vs_SMC |
0.99
|
6.468
|
4.46e-07
|
1.181
|
| Metro_vs_DEMetro_Z |
0.0
|
-26.384
|
8.02e-22
|
-4.817
|
| Metro_vs_DEMetro_Z |
0.3
|
-28.585
|
8.53e-23
|
-5.219
|
| Metro_vs_DEMetro_Z |
0.5
|
-35.836
|
1.45e-25
|
-6.543
|
| Metro_vs_DEMetro_Z |
0.9
|
-43.959
|
4.29e-28
|
-8.026
|
| Metro_vs_DEMetro_Z |
0.95
|
-30.644
|
1.21e-23
|
-5.595
|
| Metro_vs_DEMetro_Z |
0.99
|
-20.604
|
7.32e-19
|
-3.762
|
| HMC_vs_Metro |
0.0
|
-18.028
|
2.68e-17
|
-3.292
|
| HMC_vs_Metro |
0.3
|
-6.749
|
2.09e-07
|
-1.232
|
| HMC_vs_Metro |
0.5
|
-5.906
|
2.06e-06
|
-1.078
|
| HMC_vs_Metro |
0.9
|
-5.095
|
1.95e-05
|
-0.930
|
| HMC_vs_Metro |
0.95
|
-7.155
|
7.1e-08
|
-1.306
|
| HMC_vs_Metro |
0.99
|
-5.863
|
2.32e-06
|
-1.070
|
| HMC_vs_SMC |
0.0
|
-6.255
|
7.93e-07
|
-1.142
|
| HMC_vs_SMC |
0.3
|
2.220
|
0.0344
|
0.405
|
| HMC_vs_SMC |
0.5
|
3.027
|
0.00515
|
0.553
|
| HMC_vs_SMC |
0.9
|
3.828
|
0.000636
|
0.699
|
| HMC_vs_SMC |
0.95
|
5.949
|
1.83e-06
|
1.086
|
| HMC_vs_SMC |
0.99
|
5.396
|
8.45e-06
|
0.985
|
| DEMetro_Z_vs_SMC |
0.0
|
26.426
|
7.67e-22
|
4.825
|
| DEMetro_Z_vs_SMC |
0.3
|
28.643
|
8.06e-23
|
5.229
|
| DEMetro_Z_vs_SMC |
0.5
|
35.924
|
1.35e-25
|
6.559
|
| DEMetro_Z_vs_SMC |
0.9
|
46.733
|
7.45e-29
|
8.532
|
| DEMetro_Z_vs_SMC |
0.95
|
36.717
|
7.26e-26
|
6.704
|
| DEMetro_Z_vs_SMC |
0.99
|
29.099
|
5.18e-23
|
5.313
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.019 |
0.023 |
0.003 |
-1.551 |
| HMC |
0.3 |
0.027 |
0.023 |
0.006 |
0.767 |
| HMC |
0.5 |
0.037 |
0.021 |
0.008 |
2.151 |
| HMC |
0.9 |
0.070 |
0.019 |
0.013 |
3.806 |
| HMC |
0.95 |
0.093 |
0.020 |
0.012 |
6.118 |
| HMC |
0.99 |
0.125 |
0.019 |
0.014 |
7.371 |
| SMC |
0.0 |
0.022 |
0.023 |
0.003 |
-0.288 |
| SMC |
0.3 |
0.022 |
0.023 |
0.006 |
-0.062 |
| SMC |
0.5 |
0.026 |
0.021 |
0.008 |
0.654 |
| SMC |
0.9 |
0.023 |
0.019 |
0.013 |
0.285 |
| SMC |
0.95 |
0.021 |
0.020 |
0.012 |
0.087 |
| SMC |
0.99 |
0.015 |
0.019 |
0.014 |
-0.250 |
| Metro |
0.0 |
0.037 |
0.023 |
0.003 |
4.705 |
| Metro |
0.3 |
0.082 |
0.023 |
0.006 |
9.981 |
| Metro |
0.5 |
0.115 |
0.021 |
0.008 |
12.434 |
| Metro |
0.9 |
0.362 |
0.019 |
0.013 |
25.587 |
| Metro |
0.95 |
0.858 |
0.020 |
0.012 |
69.684 |
| Metro |
0.99 |
1.257 |
0.019 |
0.014 |
86.237 |
| DEMetro_Z |
0.0 |
11.433 |
0.023 |
0.003 |
3876.685 |
| DEMetro_Z |
0.3 |
12.004 |
0.023 |
0.006 |
2005.937 |
| DEMetro_Z |
0.5 |
11.665 |
0.021 |
0.008 |
1538.703 |
| DEMetro_Z |
0.9 |
11.729 |
0.019 |
0.013 |
873.192 |
| DEMetro_Z |
0.95 |
10.336 |
0.020 |
0.012 |
857.782 |
| DEMetro_Z |
0.99 |
10.341 |
0.019 |
0.014 |
719.048 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
9.358 |
1.76e-12 |
3.200 |
| HMC |
0.3 |
4.236 |
9.65e-05 |
1.399 |
| HMC |
0.5 |
3.475 |
0.00137 |
2.028 |
| HMC |
0.9 |
6.029 |
1.12e-06 |
5.962 |
| HMC |
0.95 |
6.055 |
1.03e-06 |
5.819 |
| HMC |
0.99 |
4.739 |
4.64e-05 |
5.156 |
| SMC |
0.0 |
-0.446 |
0.657 |
-0.137 |
| SMC |
0.3 |
0.654 |
0.515 |
0.176 |
| SMC |
0.5 |
0.758 |
0.452 |
0.189 |
| SMC |
0.9 |
2.212 |
0.0318 |
0.785 |
| SMC |
0.95 |
-2.560 |
0.0131 |
-0.625 |
| SMC |
0.99 |
0.024 |
0.981 |
0.007 |
| Metro |
0.0 |
17.071 |
1.45e-22 |
5.654 |
| Metro |
0.3 |
11.352 |
2.55e-13 |
6.625 |
| Metro |
0.5 |
7.865 |
9.19e-09 |
11.856 |
| Metro |
0.9 |
7.533 |
2.57e-08 |
28.417 |
| Metro |
0.95 |
7.472 |
3.01e-08 |
27.659 |
| Metro |
0.99 |
32.793 |
2.29e-25 |
37.266 |
| DEMetro_Z |
0.0 |
15.610 |
1.2e-15 |
6200.205 |
| DEMetro_Z |
0.3 |
11.577 |
2.16e-12 |
4716.960 |
| DEMetro_Z |
0.5 |
15.263 |
2.14e-15 |
3597.057 |
| DEMetro_Z |
0.9 |
14.765 |
5.04e-15 |
2155.139 |
| DEMetro_Z |
0.95 |
14.166 |
1.46e-14 |
1151.047 |
| DEMetro_Z |
0.99 |
12.562 |
2.96e-13 |
1024.418 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
8.834
|
1.02e-09
|
1.613
|
| HMC_vs_SMC |
0.3
|
4.144
|
0.00027
|
0.757
|
| HMC_vs_SMC |
0.5
|
3.350
|
0.00226
|
0.612
|
| HMC_vs_SMC |
0.9
|
4.786
|
4.6e-05
|
0.874
|
| HMC_vs_SMC |
0.95
|
6.494
|
4.15e-07
|
1.186
|
| HMC_vs_SMC |
0.99
|
4.477
|
0.000108
|
0.817
|
| Metro_vs_DEMetro_Z |
0.0
|
-15.598
|
1.22e-15
|
-2.848
|
| Metro_vs_DEMetro_Z |
0.3
|
-11.566
|
2.21e-12
|
-2.112
|
| Metro_vs_DEMetro_Z |
0.5
|
-15.218
|
2.32e-15
|
-2.778
|
| Metro_vs_DEMetro_Z |
0.9
|
-14.512
|
7.86e-15
|
-2.649
|
| Metro_vs_DEMetro_Z |
0.95
|
-13.878
|
2.45e-14
|
-2.534
|
| Metro_vs_DEMetro_Z |
0.99
|
-12.151
|
6.68e-13
|
-2.219
|
| HMC_vs_Metro |
0.0
|
-5.282
|
1.16e-05
|
-0.964
|
| HMC_vs_Metro |
0.3
|
-9.565
|
1.79e-10
|
-1.746
|
| HMC_vs_Metro |
0.5
|
-5.814
|
2.66e-06
|
-1.062
|
| HMC_vs_Metro |
0.9
|
-5.528
|
5.86e-06
|
-1.009
|
| HMC_vs_Metro |
0.95
|
-5.803
|
2.74e-06
|
-1.059
|
| HMC_vs_Metro |
0.99
|
-20.006
|
1.63e-18
|
-3.653
|
| HMC_vs_DEMetro_Z |
0.0
|
-15.602
|
1.21e-15
|
-2.848
|
| HMC_vs_DEMetro_Z |
0.3
|
-11.573
|
2.17e-12
|
-2.113
|
| HMC_vs_DEMetro_Z |
0.5
|
-15.257
|
2.17e-15
|
-2.786
|
| HMC_vs_DEMetro_Z |
0.9
|
-14.724
|
5.42e-15
|
-2.688
|
| HMC_vs_DEMetro_Z |
0.95
|
-14.078
|
1.7e-14
|
-2.570
|
| HMC_vs_DEMetro_Z |
0.99
|
-12.480
|
3.47e-13
|
-2.279
|
| Metro_vs_SMC |
0.0
|
14.953
|
3.64e-15
|
2.730
|
| Metro_vs_SMC |
0.3
|
10.842
|
1.02e-11
|
1.979
|
| Metro_vs_SMC |
0.5
|
7.608
|
2.18e-08
|
1.389
|
| Metro_vs_SMC |
0.9
|
7.216
|
6.05e-08
|
1.318
|
| Metro_vs_SMC |
0.95
|
7.683
|
1.8e-08
|
1.403
|
| Metro_vs_SMC |
0.99
|
30.184
|
1.85e-23
|
5.511
|
| DEMetro_Z_vs_SMC |
0.0
|
15.606
|
1.2e-15
|
2.849
|
| DEMetro_Z_vs_SMC |
0.3
|
11.576
|
2.16e-12
|
2.114
|
| DEMetro_Z_vs_SMC |
0.5
|
15.265
|
2.14e-15
|
2.787
|
| DEMetro_Z_vs_SMC |
0.9
|
14.757
|
5.11e-15
|
2.694
|
| DEMetro_Z_vs_SMC |
0.95
|
14.177
|
1.43e-14
|
2.588
|
| DEMetro_Z_vs_SMC |
0.99
|
12.558
|
2.98e-13
|
2.293
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.043 |
0.032 |
0.004 |
3.200 |
| HMC |
0.3 |
0.037 |
0.031 |
0.004 |
1.399 |
| HMC |
0.5 |
0.041 |
0.030 |
0.005 |
2.028 |
| HMC |
0.9 |
0.079 |
0.024 |
0.009 |
5.962 |
| HMC |
0.95 |
0.133 |
0.035 |
0.017 |
5.819 |
| HMC |
0.99 |
0.143 |
0.031 |
0.022 |
5.156 |
| SMC |
0.0 |
0.031 |
0.032 |
0.004 |
-0.137 |
| SMC |
0.3 |
0.032 |
0.031 |
0.004 |
0.176 |
| SMC |
0.5 |
0.031 |
0.030 |
0.005 |
0.189 |
| SMC |
0.9 |
0.031 |
0.024 |
0.009 |
0.785 |
| SMC |
0.95 |
0.024 |
0.035 |
0.017 |
-0.625 |
| SMC |
0.99 |
0.032 |
0.031 |
0.022 |
0.007 |
| Metro |
0.0 |
0.052 |
0.032 |
0.004 |
5.654 |
| Metro |
0.3 |
0.060 |
0.031 |
0.004 |
6.625 |
| Metro |
0.5 |
0.092 |
0.030 |
0.005 |
11.856 |
| Metro |
0.9 |
0.287 |
0.024 |
0.009 |
28.417 |
| Metro |
0.95 |
0.505 |
0.035 |
0.017 |
27.659 |
| Metro |
0.99 |
0.835 |
0.031 |
0.022 |
37.266 |
| DEMetro_Z |
0.0 |
22.017 |
0.032 |
0.004 |
6200.205 |
| DEMetro_Z |
0.3 |
20.413 |
0.031 |
0.004 |
4716.960 |
| DEMetro_Z |
0.5 |
18.892 |
0.030 |
0.005 |
3597.057 |
| DEMetro_Z |
0.9 |
20.025 |
0.024 |
0.009 |
2155.139 |
| DEMetro_Z |
0.95 |
19.597 |
0.035 |
0.017 |
1151.047 |
| DEMetro_Z |
0.99 |
22.110 |
0.031 |
0.022 |
1024.418 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.031 |
0.0472 |
-0.465 |
| HMC |
0.3 |
3.100 |
0.00339 |
1.237 |
| HMC |
0.5 |
5.788 |
9.87e-07 |
2.671 |
| HMC |
0.9 |
5.552 |
4.7e-06 |
6.608 |
| HMC |
0.95 |
9.272 |
2.16e-10 |
10.438 |
| HMC |
0.99 |
6.841 |
1.49e-07 |
13.355 |
| SMC |
0.0 |
-1.686 |
0.0972 |
-0.412 |
| SMC |
0.3 |
-0.221 |
0.826 |
-0.063 |
| SMC |
0.5 |
1.980 |
0.0534 |
0.699 |
| SMC |
0.9 |
1.734 |
0.0883 |
0.471 |
| SMC |
0.95 |
0.135 |
0.893 |
0.035 |
| SMC |
0.99 |
-0.285 |
0.777 |
-0.075 |
| Metro |
0.0 |
15.741 |
5.59e-20 |
5.930 |
| Metro |
0.3 |
7.237 |
5.11e-08 |
13.457 |
| Metro |
0.5 |
8.212 |
4.2e-09 |
17.431 |
| Metro |
0.9 |
7.666 |
1.85e-08 |
41.923 |
| Metro |
0.95 |
8.676 |
1.48e-09 |
94.176 |
| Metro |
0.99 |
7.309 |
4.73e-08 |
136.833 |
| DEMetro_Z |
0.0 |
26.009 |
1.19e-21 |
5552.249 |
| DEMetro_Z |
0.3 |
30.287 |
1.68e-23 |
2965.179 |
| DEMetro_Z |
0.5 |
41.006 |
3.12e-27 |
2212.991 |
| DEMetro_Z |
0.9 |
43.781 |
4.8e-28 |
1299.595 |
| DEMetro_Z |
0.95 |
37.706 |
3.4e-26 |
1154.947 |
| DEMetro_Z |
0.99 |
30.894 |
9.59e-24 |
1101.955 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-25.977
|
1.24e-21
|
-4.743
|
| Metro_vs_DEMetro_Z |
0.3
|
-30.228
|
1.78e-23
|
-5.519
|
| Metro_vs_DEMetro_Z |
0.5
|
-41.042
|
3.05e-27
|
-7.493
|
| Metro_vs_DEMetro_Z |
0.9
|
-41.075
|
2.98e-27
|
-7.499
|
| Metro_vs_DEMetro_Z |
0.95
|
-31.639
|
4.91e-24
|
-5.776
|
| Metro_vs_DEMetro_Z |
0.99
|
-21.880
|
1.42e-19
|
-3.995
|
| DEMetro_Z_vs_SMC |
0.0
|
26.018
|
1.18e-21
|
4.750
|
| DEMetro_Z_vs_SMC |
0.3
|
30.288
|
1.68e-23
|
5.530
|
| DEMetro_Z_vs_SMC |
0.5
|
41.023
|
3.09e-27
|
7.490
|
| DEMetro_Z_vs_SMC |
0.9
|
43.781
|
4.82e-28
|
7.993
|
| DEMetro_Z_vs_SMC |
0.95
|
37.768
|
3.25e-26
|
6.895
|
| DEMetro_Z_vs_SMC |
0.99
|
30.929
|
9.31e-24
|
5.647
|
| HMC_vs_DEMetro_Z |
0.0
|
-26.004
|
1.2e-21
|
-4.748
|
| HMC_vs_DEMetro_Z |
0.3
|
-30.299
|
1.66e-23
|
-5.532
|
| HMC_vs_DEMetro_Z |
0.5
|
-40.940
|
3.27e-27
|
-7.475
|
| HMC_vs_DEMetro_Z |
0.9
|
-44.078
|
3.97e-28
|
-8.047
|
| HMC_vs_DEMetro_Z |
0.95
|
-37.353
|
4.46e-26
|
-6.820
|
| HMC_vs_DEMetro_Z |
0.99
|
-30.400
|
1.51e-23
|
-5.550
|
| HMC_vs_Metro |
0.0
|
-17.449
|
6.4e-17
|
-3.186
|
| HMC_vs_Metro |
0.3
|
-6.635
|
2.84e-07
|
-1.211
|
| HMC_vs_Metro |
0.5
|
-6.680
|
2.52e-07
|
-1.220
|
| HMC_vs_Metro |
0.9
|
-6.344
|
6.22e-07
|
-1.158
|
| HMC_vs_Metro |
0.95
|
-7.657
|
1.92e-08
|
-1.398
|
| HMC_vs_Metro |
0.99
|
-6.530
|
3.76e-07
|
-1.192
|
| HMC_vs_SMC |
0.0
|
-0.295
|
0.77
|
-0.054
|
| HMC_vs_SMC |
0.3
|
3.125
|
0.00401
|
0.571
|
| HMC_vs_SMC |
0.5
|
3.583
|
0.00123
|
0.654
|
| HMC_vs_SMC |
0.9
|
5.237
|
1.31e-05
|
0.956
|
| HMC_vs_SMC |
0.95
|
9.441
|
2.39e-10
|
1.724
|
| HMC_vs_SMC |
0.99
|
6.812
|
1.76e-07
|
1.244
|
| Metro_vs_SMC |
0.0
|
17.267
|
8.45e-17
|
3.152
|
| Metro_vs_SMC |
0.3
|
7.069
|
8.92e-08
|
1.291
|
| Metro_vs_SMC |
0.5
|
8.341
|
3.41e-09
|
1.523
|
| Metro_vs_SMC |
0.9
|
7.601
|
2.22e-08
|
1.388
|
| Metro_vs_SMC |
0.95
|
8.670
|
1.52e-09
|
1.583
|
| Metro_vs_SMC |
0.99
|
7.292
|
4.96e-08
|
1.331
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.029 |
0.029 |
0.002 |
-0.465 |
| HMC |
0.3 |
0.033 |
0.029 |
0.003 |
1.237 |
| HMC |
0.5 |
0.039 |
0.027 |
0.004 |
2.671 |
| HMC |
0.9 |
0.073 |
0.024 |
0.007 |
6.608 |
| HMC |
0.95 |
0.103 |
0.025 |
0.007 |
10.438 |
| HMC |
0.99 |
0.129 |
0.024 |
0.008 |
13.355 |
| SMC |
0.0 |
0.029 |
0.029 |
0.002 |
-0.412 |
| SMC |
0.3 |
0.029 |
0.029 |
0.003 |
-0.063 |
| SMC |
0.5 |
0.030 |
0.027 |
0.004 |
0.699 |
| SMC |
0.9 |
0.028 |
0.024 |
0.007 |
0.471 |
| SMC |
0.95 |
0.025 |
0.025 |
0.007 |
0.035 |
| SMC |
0.99 |
0.024 |
0.024 |
0.008 |
-0.075 |
| Metro |
0.0 |
0.039 |
0.029 |
0.002 |
5.930 |
| Metro |
0.3 |
0.074 |
0.029 |
0.003 |
13.457 |
| Metro |
0.5 |
0.102 |
0.027 |
0.004 |
17.431 |
| Metro |
0.9 |
0.335 |
0.024 |
0.007 |
41.923 |
| Metro |
0.95 |
0.725 |
0.025 |
0.007 |
94.176 |
| Metro |
0.99 |
1.093 |
0.024 |
0.008 |
136.833 |
| DEMetro_Z |
0.0 |
9.540 |
0.029 |
0.002 |
5552.249 |
| DEMetro_Z |
0.3 |
9.888 |
0.029 |
0.003 |
2965.179 |
| DEMetro_Z |
0.5 |
9.574 |
0.027 |
0.004 |
2212.991 |
| DEMetro_Z |
0.9 |
9.669 |
0.024 |
0.007 |
1299.595 |
| DEMetro_Z |
0.95 |
8.612 |
0.025 |
0.007 |
1154.947 |
| DEMetro_Z |
0.99 |
8.628 |
0.024 |
0.008 |
1101.955 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.575 |
0.0132 |
-0.550 |
| HMC |
0.3 |
2.780 |
0.00807 |
1.151 |
| HMC |
0.5 |
5.362 |
4.57e-06 |
2.777 |
| HMC |
0.9 |
6.444 |
3.61e-07 |
6.819 |
| HMC |
0.95 |
8.717 |
8.75e-10 |
9.963 |
| HMC |
0.99 |
6.354 |
5.45e-07 |
10.641 |
| SMC |
0.0 |
-1.287 |
0.203 |
-0.315 |
| SMC |
0.3 |
-0.128 |
0.899 |
-0.036 |
| SMC |
0.5 |
2.359 |
0.0225 |
0.836 |
| SMC |
0.9 |
2.104 |
0.0399 |
0.590 |
| SMC |
0.95 |
0.045 |
0.964 |
0.012 |
| SMC |
0.99 |
-0.401 |
0.69 |
-0.102 |
| Metro |
0.0 |
13.931 |
3.2e-19 |
4.404 |
| Metro |
0.3 |
7.606 |
1.84e-08 |
11.985 |
| Metro |
0.5 |
8.990 |
5.99e-10 |
17.806 |
| Metro |
0.9 |
9.588 |
1.64e-10 |
41.564 |
| Metro |
0.95 |
11.658 |
1.78e-12 |
76.503 |
| Metro |
0.99 |
16.229 |
4.2e-16 |
109.348 |
| DEMetro_Z |
0.0 |
78.194 |
2.53e-35 |
547.518 |
| DEMetro_Z |
0.3 |
80.435 |
1e-35 |
375.008 |
| DEMetro_Z |
0.5 |
58.947 |
8.44e-32 |
329.757 |
| DEMetro_Z |
0.9 |
78.125 |
1.46e-35 |
198.418 |
| DEMetro_Z |
0.95 |
124.903 |
2.38e-42 |
172.828 |
| DEMetro_Z |
0.99 |
97.253 |
5.76e-39 |
143.415 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
78.813
|
2.2e-35
|
14.389
|
| DEMetro_Z_vs_SMC |
0.3
|
80.340
|
1.26e-35
|
14.668
|
| DEMetro_Z_vs_SMC |
0.5
|
59.418
|
7.56e-32
|
10.848
|
| DEMetro_Z_vs_SMC |
0.9
|
76.538
|
5.12e-35
|
13.974
|
| DEMetro_Z_vs_SMC |
0.95
|
119.499
|
1.31e-40
|
21.817
|
| DEMetro_Z_vs_SMC |
0.99
|
97.911
|
4.16e-38
|
17.876
|
| HMC_vs_Metro |
0.0
|
-16.354
|
3.54e-16
|
-2.986
|
| HMC_vs_Metro |
0.3
|
-6.987
|
1.11e-07
|
-1.276
|
| HMC_vs_Metro |
0.5
|
-7.320
|
4.61e-08
|
-1.336
|
| HMC_vs_Metro |
0.9
|
-7.982
|
8.38e-09
|
-1.457
|
| HMC_vs_Metro |
0.95
|
-9.732
|
1.22e-10
|
-1.777
|
| HMC_vs_Metro |
0.99
|
-14.150
|
1.5e-14
|
-2.583
|
| Metro_vs_DEMetro_Z |
0.0
|
-77.249
|
3.92e-35
|
-14.104
|
| Metro_vs_DEMetro_Z |
0.3
|
-69.684
|
7.67e-34
|
-12.723
|
| Metro_vs_DEMetro_Z |
0.5
|
-57.918
|
1.58e-31
|
-10.574
|
| Metro_vs_DEMetro_Z |
0.9
|
-30.150
|
1.91e-23
|
-5.505
|
| Metro_vs_DEMetro_Z |
0.95
|
-14.204
|
1.36e-14
|
-2.593
|
| Metro_vs_DEMetro_Z |
0.99
|
-4.842
|
3.94e-05
|
-0.884
|
| HMC_vs_SMC |
0.0
|
-1.453
|
0.157
|
-0.265
|
| HMC_vs_SMC |
0.3
|
2.756
|
0.01
|
0.503
|
| HMC_vs_SMC |
0.5
|
3.303
|
0.00255
|
0.603
|
| HMC_vs_SMC |
0.9
|
5.881
|
2.21e-06
|
1.074
|
| HMC_vs_SMC |
0.95
|
9.206
|
4.17e-10
|
1.681
|
| HMC_vs_SMC |
0.99
|
6.356
|
6.03e-07
|
1.160
|
| Metro_vs_SMC |
0.0
|
14.838
|
4.45e-15
|
2.709
|
| Metro_vs_SMC |
0.3
|
7.335
|
4.43e-08
|
1.339
|
| Metro_vs_SMC |
0.5
|
8.997
|
6.87e-10
|
1.643
|
| Metro_vs_SMC |
0.9
|
9.614
|
1.6e-10
|
1.755
|
| Metro_vs_SMC |
0.95
|
11.624
|
1.95e-12
|
2.122
|
| Metro_vs_SMC |
0.99
|
16.172
|
4.75e-16
|
2.953
|
| HMC_vs_DEMetro_Z |
0.0
|
-78.435
|
2.53e-35
|
-14.320
|
| HMC_vs_DEMetro_Z |
0.3
|
-80.472
|
1.2e-35
|
-14.692
|
| HMC_vs_DEMetro_Z |
0.5
|
-57.207
|
2.25e-31
|
-10.444
|
| HMC_vs_DEMetro_Z |
0.9
|
-66.275
|
3.25e-33
|
-12.100
|
| HMC_vs_DEMetro_Z |
0.95
|
-90.003
|
4.75e-37
|
-16.432
|
| HMC_vs_DEMetro_Z |
0.99
|
-58.500
|
1.18e-31
|
-10.681
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.013 |
0.014 |
0.002 |
-0.550 |
| HMC |
0.3 |
0.017 |
0.015 |
0.002 |
1.151 |
| HMC |
0.5 |
0.022 |
0.014 |
0.003 |
2.777 |
| HMC |
0.9 |
0.046 |
0.014 |
0.005 |
6.819 |
| HMC |
0.95 |
0.069 |
0.015 |
0.005 |
9.963 |
| HMC |
0.99 |
0.082 |
0.014 |
0.006 |
10.641 |
| SMC |
0.0 |
0.014 |
0.014 |
0.002 |
-0.315 |
| SMC |
0.3 |
0.014 |
0.015 |
0.002 |
-0.036 |
| SMC |
0.5 |
0.016 |
0.014 |
0.003 |
0.836 |
| SMC |
0.9 |
0.016 |
0.014 |
0.005 |
0.590 |
| SMC |
0.95 |
0.015 |
0.015 |
0.005 |
0.012 |
| SMC |
0.99 |
0.014 |
0.014 |
0.006 |
-0.102 |
| Metro |
0.0 |
0.022 |
0.014 |
0.002 |
4.404 |
| Metro |
0.3 |
0.044 |
0.015 |
0.002 |
11.985 |
| Metro |
0.5 |
0.064 |
0.014 |
0.003 |
17.806 |
| Metro |
0.9 |
0.212 |
0.014 |
0.005 |
41.564 |
| Metro |
0.95 |
0.428 |
0.015 |
0.005 |
76.503 |
| Metro |
0.99 |
0.708 |
0.014 |
0.006 |
109.348 |
| DEMetro_Z |
0.0 |
0.945 |
0.014 |
0.002 |
547.518 |
| DEMetro_Z |
0.3 |
0.944 |
0.015 |
0.002 |
375.008 |
| DEMetro_Z |
0.5 |
0.933 |
0.014 |
0.003 |
329.757 |
| DEMetro_Z |
0.9 |
0.960 |
0.014 |
0.005 |
198.418 |
| DEMetro_Z |
0.95 |
0.948 |
0.015 |
0.005 |
172.828 |
| DEMetro_Z |
0.99 |
0.924 |
0.014 |
0.006 |
143.415 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
0.5
0.9
0.95
0.99
Vary_Correlation_with_heavy_Tails
(MvStudentT,
correlation,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.044 |
0.965 |
-0.012 |
| HMC |
0.3 |
2.068 |
0.0439 |
0.709 |
| HMC |
0.5 |
1.719 |
0.0912 |
0.513 |
| HMC |
0.9 |
3.252 |
0.00242 |
1.631 |
| HMC |
0.95 |
3.565 |
0.000957 |
1.591 |
| HMC |
0.99 |
2.277 |
0.0274 |
0.815 |
| SMC |
0.0 |
-0.826 |
0.413 |
-0.186 |
| SMC |
0.3 |
-0.590 |
0.558 |
-0.130 |
| SMC |
0.5 |
0.160 |
0.874 |
0.040 |
| SMC |
0.9 |
1.043 |
0.302 |
0.324 |
| SMC |
0.95 |
0.493 |
0.624 |
0.114 |
| SMC |
0.99 |
-0.084 |
0.934 |
-0.027 |
| Metro |
0.0 |
1.882 |
0.0673 |
0.886 |
| Metro |
0.3 |
3.754 |
0.000632 |
2.220 |
| Metro |
0.5 |
2.602 |
0.0128 |
1.095 |
| Metro |
0.9 |
1.789 |
0.0841 |
16.066 |
| Metro |
0.95 |
4.192 |
0.000232 |
9.673 |
| Metro |
0.99 |
4.511 |
9.82e-05 |
28.951 |
| DEMetro_Z |
0.0 |
3.308 |
0.00202 |
1.537 |
| DEMetro_Z |
0.3 |
3.426 |
0.00153 |
1.815 |
| DEMetro_Z |
0.5 |
3.894 |
0.000315 |
1.426 |
| DEMetro_Z |
0.9 |
3.525 |
0.00133 |
3.339 |
| DEMetro_Z |
0.95 |
4.279 |
0.000125 |
2.175 |
| DEMetro_Z |
0.99 |
3.622 |
0.00101 |
3.089 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-3.266
|
0.0028
|
-0.596
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.234
|
0.0334
|
-0.408
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.340
|
0.0264
|
-0.427
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.661
|
0.108
|
-0.303
|
| HMC_vs_DEMetro_Z |
0.95
|
-0.953
|
0.348
|
-0.174
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.592
|
0.0148
|
-0.473
|
| Metro_vs_SMC |
0.0
|
2.396
|
0.0233
|
0.437
|
| Metro_vs_SMC |
0.3
|
4.151
|
0.000265
|
0.758
|
| Metro_vs_SMC |
0.5
|
2.661
|
0.0126
|
0.486
|
| Metro_vs_SMC |
0.9
|
1.750
|
0.0907
|
0.319
|
| Metro_vs_SMC |
0.95
|
4.113
|
0.000294
|
0.751
|
| Metro_vs_SMC |
0.99
|
4.545
|
8.97e-05
|
0.830
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.964
|
0.343
|
-0.176
|
| Metro_vs_DEMetro_Z |
0.3
|
0.650
|
0.521
|
0.119
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.676
|
0.504
|
-0.123
|
| Metro_vs_DEMetro_Z |
0.9
|
1.396
|
0.173
|
0.255
|
| Metro_vs_DEMetro_Z |
0.95
|
3.184
|
0.00346
|
0.581
|
| Metro_vs_DEMetro_Z |
0.99
|
3.924
|
0.000492
|
0.716
|
| HMC_vs_Metro |
0.0
|
-1.799
|
0.0825
|
-0.328
|
| HMC_vs_Metro |
0.3
|
-2.642
|
0.0132
|
-0.482
|
| HMC_vs_Metro |
0.5
|
-1.325
|
0.195
|
-0.242
|
| HMC_vs_Metro |
0.9
|
-1.597
|
0.121
|
-0.292
|
| HMC_vs_Metro |
0.95
|
-3.421
|
0.00188
|
-0.625
|
| HMC_vs_Metro |
0.99
|
-4.347
|
0.000155
|
-0.794
|
| HMC_vs_SMC |
0.0
|
0.698
|
0.491
|
0.127
|
| HMC_vs_SMC |
0.3
|
2.762
|
0.00987
|
0.504
|
| HMC_vs_SMC |
0.5
|
2.241
|
0.0328
|
0.409
|
| HMC_vs_SMC |
0.9
|
2.554
|
0.0162
|
0.466
|
| HMC_vs_SMC |
0.95
|
3.437
|
0.0018
|
0.627
|
| HMC_vs_SMC |
0.99
|
2.060
|
0.0485
|
0.376
|
| DEMetro_Z_vs_SMC |
0.0
|
3.927
|
0.000488
|
0.717
|
| DEMetro_Z_vs_SMC |
0.3
|
4.214
|
0.000223
|
0.769
|
| DEMetro_Z_vs_SMC |
0.5
|
4.264
|
0.000195
|
0.779
|
| DEMetro_Z_vs_SMC |
0.9
|
3.149
|
0.00378
|
0.575
|
| DEMetro_Z_vs_SMC |
0.95
|
3.968
|
0.000436
|
0.724
|
| DEMetro_Z_vs_SMC |
0.99
|
3.453
|
0.00173
|
0.630
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.064 |
0.065 |
0.042 |
-0.012 |
| HMC |
0.3 |
0.084 |
0.056 |
0.040 |
0.709 |
| HMC |
0.5 |
0.092 |
0.068 |
0.046 |
0.513 |
| HMC |
0.9 |
0.090 |
0.047 |
0.027 |
1.631 |
| HMC |
0.95 |
0.112 |
0.053 |
0.037 |
1.591 |
| HMC |
0.99 |
0.099 |
0.061 |
0.047 |
0.815 |
| SMC |
0.0 |
0.057 |
0.065 |
0.042 |
-0.186 |
| SMC |
0.3 |
0.051 |
0.056 |
0.040 |
-0.130 |
| SMC |
0.5 |
0.070 |
0.068 |
0.046 |
0.040 |
| SMC |
0.9 |
0.056 |
0.047 |
0.027 |
0.324 |
| SMC |
0.95 |
0.057 |
0.053 |
0.037 |
0.114 |
| SMC |
0.99 |
0.059 |
0.061 |
0.047 |
-0.027 |
| Metro |
0.0 |
0.102 |
0.065 |
0.042 |
0.886 |
| Metro |
0.3 |
0.144 |
0.056 |
0.040 |
2.220 |
| Metro |
0.5 |
0.119 |
0.068 |
0.046 |
1.095 |
| Metro |
0.9 |
0.475 |
0.047 |
0.027 |
16.066 |
| Metro |
0.95 |
0.410 |
0.053 |
0.037 |
9.673 |
| Metro |
0.99 |
1.433 |
0.061 |
0.047 |
28.951 |
| DEMetro_Z |
0.0 |
0.129 |
0.065 |
0.042 |
1.537 |
| DEMetro_Z |
0.3 |
0.128 |
0.056 |
0.040 |
1.815 |
| DEMetro_Z |
0.5 |
0.134 |
0.068 |
0.046 |
1.426 |
| DEMetro_Z |
0.9 |
0.136 |
0.047 |
0.027 |
3.339 |
| DEMetro_Z |
0.95 |
0.133 |
0.053 |
0.037 |
2.175 |
| DEMetro_Z |
0.99 |
0.207 |
0.061 |
0.047 |
3.089 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-1.569 |
0.125 |
-0.309 |
| HMC |
0.3 |
1.396 |
0.171 |
0.672 |
| HMC |
0.5 |
1.072 |
0.293 |
1.596 |
| HMC |
0.9 |
0.151 |
0.881 |
0.043 |
| HMC |
0.95 |
0.314 |
0.755 |
0.123 |
| HMC |
0.99 |
-0.237 |
0.813 |
-0.053 |
| SMC |
0.0 |
-1.672 |
0.103 |
-0.331 |
| SMC |
0.3 |
0.541 |
0.59 |
0.148 |
| SMC |
0.5 |
0.370 |
0.713 |
0.094 |
| SMC |
0.9 |
-1.384 |
0.174 |
-0.285 |
| SMC |
0.95 |
-1.382 |
0.173 |
-0.308 |
| SMC |
0.99 |
-1.231 |
0.226 |
-0.241 |
| Metro |
0.0 |
-1.603 |
0.118 |
-0.308 |
| Metro |
0.3 |
1.097 |
0.278 |
0.381 |
| Metro |
0.5 |
0.396 |
0.694 |
0.098 |
| Metro |
0.9 |
0.995 |
0.327 |
1.248 |
| Metro |
0.95 |
0.795 |
0.432 |
0.504 |
| Metro |
0.99 |
2.425 |
0.0207 |
1.524 |
| DEMetro_Z |
0.0 |
-1.546 |
0.131 |
-0.297 |
| DEMetro_Z |
0.3 |
0.790 |
0.433 |
0.251 |
| DEMetro_Z |
0.5 |
0.537 |
0.594 |
0.135 |
| DEMetro_Z |
0.9 |
0.915 |
0.364 |
0.247 |
| DEMetro_Z |
0.95 |
-0.444 |
0.659 |
-0.100 |
| DEMetro_Z |
0.99 |
-0.564 |
0.576 |
-0.110 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
0.377
|
0.709
|
0.069
|
| HMC_vs_SMC |
0.3
|
1.212
|
0.235
|
0.221
|
| HMC_vs_SMC |
0.5
|
1.013
|
0.32
|
0.185
|
| HMC_vs_SMC |
0.9
|
1.438
|
0.161
|
0.263
|
| HMC_vs_SMC |
0.95
|
1.316
|
0.199
|
0.240
|
| HMC_vs_SMC |
0.99
|
1.501
|
0.144
|
0.274
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.303
|
0.764
|
-0.055
|
| Metro_vs_DEMetro_Z |
0.3
|
0.761
|
0.453
|
0.139
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.210
|
0.236
|
-0.221
|
| Metro_vs_DEMetro_Z |
0.9
|
0.788
|
0.437
|
0.144
|
| Metro_vs_DEMetro_Z |
0.95
|
1.025
|
0.314
|
0.187
|
| Metro_vs_DEMetro_Z |
0.99
|
2.720
|
0.0109
|
0.497
|
| HMC_vs_Metro |
0.0
|
-0.012
|
0.991
|
-0.002
|
| HMC_vs_Metro |
0.3
|
0.625
|
0.537
|
0.114
|
| HMC_vs_Metro |
0.5
|
1.020
|
0.316
|
0.186
|
| HMC_vs_Metro |
0.9
|
-0.947
|
0.352
|
-0.173
|
| HMC_vs_Metro |
0.95
|
-0.567
|
0.575
|
-0.103
|
| HMC_vs_Metro |
0.99
|
-2.516
|
0.0177
|
-0.459
|
| HMC_vs_DEMetro_Z |
0.0
|
-0.273
|
0.787
|
-0.050
|
| HMC_vs_DEMetro_Z |
0.3
|
1.024
|
0.314
|
0.187
|
| HMC_vs_DEMetro_Z |
0.5
|
0.986
|
0.332
|
0.180
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.695
|
0.492
|
-0.127
|
| HMC_vs_DEMetro_Z |
0.95
|
0.751
|
0.458
|
0.137
|
| HMC_vs_DEMetro_Z |
0.99
|
0.526
|
0.603
|
0.096
|
| Metro_vs_SMC |
0.0
|
0.395
|
0.695
|
0.072
|
| Metro_vs_SMC |
0.3
|
1.206
|
0.238
|
0.220
|
| Metro_vs_SMC |
0.5
|
0.133
|
0.895
|
0.024
|
| Metro_vs_SMC |
0.9
|
1.239
|
0.225
|
0.226
|
| Metro_vs_SMC |
0.95
|
1.401
|
0.172
|
0.256
|
| Metro_vs_SMC |
0.99
|
2.913
|
0.00683
|
0.532
|
| DEMetro_Z_vs_SMC |
0.0
|
0.696
|
0.492
|
0.127
|
| DEMetro_Z_vs_SMC |
0.3
|
0.885
|
0.383
|
0.162
|
| DEMetro_Z_vs_SMC |
0.5
|
0.942
|
0.354
|
0.172
|
| DEMetro_Z_vs_SMC |
0.9
|
3.034
|
0.00506
|
0.554
|
| DEMetro_Z_vs_SMC |
0.95
|
3.681
|
0.000943
|
0.672
|
| DEMetro_Z_vs_SMC |
0.99
|
1.674
|
0.105
|
0.306
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
4.719 |
9.112 |
14.240 |
-0.309 |
| HMC |
0.3 |
8.039 |
4.697 |
4.977 |
0.672 |
| HMC |
0.5 |
47.348 |
9.883 |
23.480 |
1.596 |
| HMC |
0.9 |
5.657 |
5.328 |
7.624 |
0.043 |
| HMC |
0.95 |
7.739 |
6.496 |
10.111 |
0.123 |
| HMC |
0.99 |
4.903 |
5.445 |
10.256 |
-0.053 |
| SMC |
0.0 |
4.403 |
9.112 |
14.240 |
-0.331 |
| SMC |
0.3 |
5.435 |
4.697 |
4.977 |
0.148 |
| SMC |
0.5 |
12.079 |
9.883 |
23.480 |
0.094 |
| SMC |
0.9 |
3.155 |
5.328 |
7.624 |
-0.285 |
| SMC |
0.95 |
3.387 |
6.496 |
10.111 |
-0.308 |
| SMC |
0.99 |
2.973 |
5.445 |
10.256 |
-0.241 |
| Metro |
0.0 |
4.727 |
9.112 |
14.240 |
-0.308 |
| Metro |
0.3 |
6.593 |
4.697 |
4.977 |
0.381 |
| Metro |
0.5 |
12.180 |
9.883 |
23.480 |
0.098 |
| Metro |
0.9 |
14.847 |
5.328 |
7.624 |
1.248 |
| Metro |
0.95 |
11.597 |
6.496 |
10.111 |
0.504 |
| Metro |
0.99 |
21.071 |
5.445 |
10.256 |
1.524 |
| DEMetro_Z |
0.0 |
4.881 |
9.112 |
14.240 |
-0.297 |
| DEMetro_Z |
0.3 |
5.946 |
4.697 |
4.977 |
0.251 |
| DEMetro_Z |
0.5 |
13.057 |
9.883 |
23.480 |
0.135 |
| DEMetro_Z |
0.9 |
7.210 |
5.328 |
7.624 |
0.247 |
| DEMetro_Z |
0.95 |
5.489 |
6.496 |
10.111 |
-0.100 |
| DEMetro_Z |
0.99 |
4.318 |
5.445 |
10.256 |
-0.110 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.949 |
0.0574 |
0.719 |
| HMC |
0.3 |
3.948 |
0.000369 |
2.424 |
| HMC |
0.5 |
1.808 |
0.0807 |
3.048 |
| HMC |
0.9 |
5.039 |
7.42e-06 |
1.820 |
| HMC |
0.95 |
4.228 |
0.000191 |
4.039 |
| HMC |
0.99 |
5.311 |
6.26e-06 |
3.153 |
| SMC |
0.0 |
-0.278 |
0.782 |
-0.066 |
| SMC |
0.3 |
0.570 |
0.571 |
0.140 |
| SMC |
0.5 |
0.943 |
0.35 |
0.256 |
| SMC |
0.9 |
-0.490 |
0.626 |
-0.118 |
| SMC |
0.95 |
0.715 |
0.478 |
0.224 |
| SMC |
0.99 |
1.616 |
0.113 |
0.557 |
| Metro |
0.0 |
4.926 |
1.85e-05 |
2.680 |
| Metro |
0.3 |
6.119 |
6.38e-07 |
4.142 |
| Metro |
0.5 |
7.400 |
3.78e-09 |
3.060 |
| Metro |
0.9 |
2.300 |
0.0288 |
14.581 |
| Metro |
0.95 |
5.805 |
2.64e-06 |
15.821 |
| Metro |
0.99 |
5.682 |
3.81e-06 |
41.783 |
| DEMetro_Z |
0.0 |
8.153 |
6.49e-10 |
3.917 |
| DEMetro_Z |
0.3 |
8.543 |
5.35e-10 |
5.423 |
| DEMetro_Z |
0.5 |
8.995 |
5.35e-11 |
4.335 |
| DEMetro_Z |
0.9 |
4.955 |
2.54e-05 |
5.691 |
| DEMetro_Z |
0.95 |
9.087 |
2.23e-10 |
7.465 |
| DEMetro_Z |
0.99 |
6.116 |
8.26e-07 |
5.469 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-1.657
|
0.108
|
-0.302
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.478
|
0.15
|
-0.270
|
| Metro_vs_DEMetro_Z |
0.5
|
-2.637
|
0.0133
|
-0.481
|
| Metro_vs_DEMetro_Z |
0.9
|
1.350
|
0.187
|
0.247
|
| Metro_vs_DEMetro_Z |
0.95
|
2.943
|
0.00634
|
0.537
|
| Metro_vs_DEMetro_Z |
0.99
|
4.802
|
4.39e-05
|
0.877
|
| DEMetro_Z_vs_SMC |
0.0
|
8.149
|
5.5e-09
|
1.488
|
| DEMetro_Z_vs_SMC |
0.3
|
9.011
|
6.63e-10
|
1.645
|
| DEMetro_Z_vs_SMC |
0.5
|
9.290
|
3.41e-10
|
1.696
|
| DEMetro_Z_vs_SMC |
0.9
|
5.152
|
1.66e-05
|
0.941
|
| DEMetro_Z_vs_SMC |
0.95
|
9.055
|
5.97e-10
|
1.653
|
| DEMetro_Z_vs_SMC |
0.99
|
5.166
|
1.6e-05
|
0.943
|
| HMC_vs_DEMetro_Z |
0.0
|
-5.863
|
2.32e-06
|
-1.070
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.495
|
0.00155
|
-0.638
|
| HMC_vs_DEMetro_Z |
0.5
|
-0.720
|
0.477
|
-0.131
|
| HMC_vs_DEMetro_Z |
0.9
|
-3.435
|
0.00181
|
-0.627
|
| HMC_vs_DEMetro_Z |
0.95
|
-4.524
|
9.51e-05
|
-0.826
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.129
|
0.0419
|
-0.389
|
| HMC_vs_Metro |
0.0
|
-3.468
|
0.00166
|
-0.633
|
| HMC_vs_Metro |
0.3
|
-2.150
|
0.0401
|
-0.392
|
| HMC_vs_Metro |
0.5
|
-0.008
|
0.994
|
-0.001
|
| HMC_vs_Metro |
0.9
|
-2.014
|
0.0534
|
-0.368
|
| HMC_vs_Metro |
0.95
|
-3.986
|
0.000415
|
-0.728
|
| HMC_vs_Metro |
0.99
|
-5.236
|
1.32e-05
|
-0.956
|
| HMC_vs_SMC |
0.0
|
2.384
|
0.0239
|
0.435
|
| HMC_vs_SMC |
0.3
|
3.525
|
0.00143
|
0.643
|
| HMC_vs_SMC |
0.5
|
1.660
|
0.108
|
0.303
|
| HMC_vs_SMC |
0.9
|
6.305
|
6.93e-07
|
1.151
|
| HMC_vs_SMC |
0.95
|
4.030
|
0.000368
|
0.736
|
| HMC_vs_SMC |
0.99
|
3.834
|
0.000627
|
0.700
|
| Metro_vs_SMC |
0.0
|
5.373
|
9.01e-06
|
0.981
|
| Metro_vs_SMC |
0.3
|
6.450
|
4.67e-07
|
1.178
|
| Metro_vs_SMC |
0.5
|
8.808
|
1.08e-09
|
1.608
|
| Metro_vs_SMC |
0.9
|
2.313
|
0.028
|
0.422
|
| Metro_vs_SMC |
0.95
|
5.746
|
3.2e-06
|
1.049
|
| Metro_vs_SMC |
0.99
|
5.609
|
4.68e-06
|
1.024
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.149 |
0.124 |
0.035 |
0.719 |
| HMC |
0.3 |
0.182 |
0.116 |
0.027 |
2.424 |
| HMC |
0.5 |
0.230 |
0.120 |
0.036 |
3.048 |
| HMC |
0.9 |
0.176 |
0.115 |
0.034 |
1.820 |
| HMC |
0.95 |
0.210 |
0.111 |
0.025 |
4.039 |
| HMC |
0.99 |
0.236 |
0.111 |
0.040 |
3.153 |
| SMC |
0.0 |
0.122 |
0.124 |
0.035 |
-0.066 |
| SMC |
0.3 |
0.120 |
0.116 |
0.027 |
0.140 |
| SMC |
0.5 |
0.129 |
0.120 |
0.036 |
0.256 |
| SMC |
0.9 |
0.111 |
0.115 |
0.034 |
-0.118 |
| SMC |
0.95 |
0.116 |
0.111 |
0.025 |
0.224 |
| SMC |
0.99 |
0.133 |
0.111 |
0.040 |
0.557 |
| Metro |
0.0 |
0.217 |
0.124 |
0.035 |
2.680 |
| Metro |
0.3 |
0.229 |
0.116 |
0.027 |
4.142 |
| Metro |
0.5 |
0.231 |
0.120 |
0.036 |
3.060 |
| Metro |
0.9 |
0.605 |
0.115 |
0.034 |
14.581 |
| Metro |
0.95 |
0.499 |
0.111 |
0.025 |
15.821 |
| Metro |
0.99 |
1.763 |
0.111 |
0.040 |
41.783 |
| DEMetro_Z |
0.0 |
0.261 |
0.124 |
0.035 |
3.917 |
| DEMetro_Z |
0.3 |
0.263 |
0.116 |
0.027 |
5.423 |
| DEMetro_Z |
0.5 |
0.277 |
0.120 |
0.036 |
4.335 |
| DEMetro_Z |
0.9 |
0.306 |
0.115 |
0.034 |
5.691 |
| DEMetro_Z |
0.95 |
0.294 |
0.111 |
0.025 |
7.465 |
| DEMetro_Z |
0.99 |
0.327 |
0.111 |
0.040 |
5.469 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.850 |
0.00609 |
0.687 |
| HMC |
0.3 |
2.509 |
0.0175 |
2.346 |
| HMC |
0.5 |
3.705 |
0.000533 |
1.250 |
| HMC |
0.9 |
6.222 |
1.04e-07 |
2.111 |
| HMC |
0.95 |
5.630 |
2e-06 |
2.936 |
| HMC |
0.99 |
6.065 |
2.67e-07 |
2.359 |
| SMC |
0.0 |
1.382 |
0.173 |
0.462 |
| SMC |
0.3 |
2.033 |
0.0473 |
0.656 |
| SMC |
0.5 |
0.886 |
0.379 |
0.271 |
| SMC |
0.9 |
1.768 |
0.0825 |
0.506 |
| SMC |
0.95 |
5.059 |
8.06e-06 |
1.998 |
| SMC |
0.99 |
3.984 |
0.000257 |
1.600 |
| Metro |
0.0 |
8.124 |
8.92e-10 |
4.144 |
| Metro |
0.3 |
7.986 |
1.57e-09 |
4.269 |
| Metro |
0.5 |
7.556 |
1.02e-08 |
5.231 |
| Metro |
0.9 |
8.272 |
3.21e-09 |
12.398 |
| Metro |
0.95 |
9.779 |
8.96e-11 |
18.260 |
| Metro |
0.99 |
13.732 |
2.66e-14 |
34.098 |
| DEMetro_Z |
0.0 |
8.360 |
1.17e-09 |
5.987 |
| DEMetro_Z |
0.3 |
7.438 |
1.98e-08 |
6.552 |
| DEMetro_Z |
0.5 |
10.003 |
1.42e-11 |
6.876 |
| DEMetro_Z |
0.9 |
5.997 |
1.31e-06 |
6.756 |
| DEMetro_Z |
0.95 |
9.107 |
3.21e-10 |
10.135 |
| DEMetro_Z |
0.99 |
7.979 |
4.27e-09 |
6.687 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
7.036
|
9.74e-08
|
1.285
|
| DEMetro_Z_vs_SMC |
0.3
|
6.688
|
2.46e-07
|
1.221
|
| DEMetro_Z_vs_SMC |
0.5
|
9.400
|
2.64e-10
|
1.716
|
| DEMetro_Z_vs_SMC |
0.9
|
6.002
|
1.58e-06
|
1.096
|
| DEMetro_Z_vs_SMC |
0.95
|
7.330
|
4.48e-08
|
1.338
|
| DEMetro_Z_vs_SMC |
0.99
|
5.886
|
2.18e-06
|
1.075
|
| HMC_vs_Metro |
0.0
|
-7.322
|
4.59e-08
|
-1.337
|
| HMC_vs_Metro |
0.3
|
-2.289
|
0.0296
|
-0.418
|
| HMC_vs_Metro |
0.5
|
-5.749
|
3.18e-06
|
-1.050
|
| HMC_vs_Metro |
0.9
|
-6.643
|
2.77e-07
|
-1.213
|
| HMC_vs_Metro |
0.95
|
-8.552
|
2.02e-09
|
-1.561
|
| HMC_vs_Metro |
0.99
|
-12.600
|
2.74e-13
|
-2.300
|
| Metro_vs_DEMetro_Z |
0.0
|
-2.192
|
0.0365
|
-0.400
|
| Metro_vs_DEMetro_Z |
0.3
|
-2.128
|
0.042
|
-0.388
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.700
|
0.0998
|
-0.310
|
| Metro_vs_DEMetro_Z |
0.9
|
2.812
|
0.00874
|
0.513
|
| Metro_vs_DEMetro_Z |
0.95
|
4.091
|
0.000312
|
0.747
|
| Metro_vs_DEMetro_Z |
0.99
|
9.650
|
1.47e-10
|
1.762
|
| HMC_vs_SMC |
0.0
|
0.765
|
0.45
|
0.140
|
| HMC_vs_SMC |
0.3
|
1.780
|
0.0856
|
0.325
|
| HMC_vs_SMC |
0.5
|
2.601
|
0.0145
|
0.475
|
| HMC_vs_SMC |
0.9
|
3.991
|
0.00041
|
0.729
|
| HMC_vs_SMC |
0.95
|
1.443
|
0.16
|
0.263
|
| HMC_vs_SMC |
0.99
|
1.343
|
0.19
|
0.245
|
| Metro_vs_SMC |
0.0
|
8.791
|
1.13e-09
|
1.605
|
| Metro_vs_SMC |
0.3
|
6.833
|
1.67e-07
|
1.247
|
| Metro_vs_SMC |
0.5
|
7.919
|
9.84e-09
|
1.446
|
| Metro_vs_SMC |
0.9
|
7.826
|
1.25e-08
|
1.429
|
| Metro_vs_SMC |
0.95
|
8.422
|
2.78e-09
|
1.538
|
| Metro_vs_SMC |
0.99
|
12.820
|
1.79e-13
|
2.341
|
| HMC_vs_DEMetro_Z |
0.0
|
-6.988
|
1.11e-07
|
-1.276
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.231
|
0.00307
|
-0.590
|
| HMC_vs_DEMetro_Z |
0.5
|
-8.158
|
5.38e-09
|
-1.489
|
| HMC_vs_DEMetro_Z |
0.9
|
-4.213
|
0.000224
|
-0.769
|
| HMC_vs_DEMetro_Z |
0.95
|
-6.518
|
3.89e-07
|
-1.190
|
| HMC_vs_DEMetro_Z |
0.99
|
-4.357
|
0.000151
|
-0.796
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.018 |
0.015 |
0.005 |
0.687 |
| HMC |
0.3 |
0.024 |
0.015 |
0.004 |
2.346 |
| HMC |
0.5 |
0.020 |
0.015 |
0.004 |
1.250 |
| HMC |
0.9 |
0.024 |
0.014 |
0.005 |
2.111 |
| HMC |
0.95 |
0.025 |
0.014 |
0.004 |
2.936 |
| HMC |
0.99 |
0.032 |
0.015 |
0.007 |
2.359 |
| SMC |
0.0 |
0.017 |
0.015 |
0.005 |
0.462 |
| SMC |
0.3 |
0.017 |
0.015 |
0.004 |
0.656 |
| SMC |
0.5 |
0.016 |
0.015 |
0.004 |
0.271 |
| SMC |
0.9 |
0.017 |
0.014 |
0.005 |
0.506 |
| SMC |
0.95 |
0.021 |
0.014 |
0.004 |
1.998 |
| SMC |
0.99 |
0.027 |
0.015 |
0.007 |
1.600 |
| Metro |
0.0 |
0.034 |
0.015 |
0.005 |
4.144 |
| Metro |
0.3 |
0.032 |
0.015 |
0.004 |
4.269 |
| Metro |
0.5 |
0.036 |
0.015 |
0.004 |
5.231 |
| Metro |
0.9 |
0.073 |
0.014 |
0.005 |
12.398 |
| Metro |
0.95 |
0.081 |
0.014 |
0.004 |
18.260 |
| Metro |
0.99 |
0.257 |
0.015 |
0.007 |
34.098 |
| DEMetro_Z |
0.0 |
0.042 |
0.015 |
0.005 |
5.987 |
| DEMetro_Z |
0.3 |
0.042 |
0.015 |
0.004 |
6.552 |
| DEMetro_Z |
0.5 |
0.042 |
0.015 |
0.004 |
6.876 |
| DEMetro_Z |
0.9 |
0.046 |
0.014 |
0.005 |
6.756 |
| DEMetro_Z |
0.95 |
0.051 |
0.014 |
0.004 |
10.135 |
| DEMetro_Z |
0.99 |
0.063 |
0.015 |
0.007 |
6.687 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.144 |
0.886 |
0.037 |
| HMC |
0.3 |
1.196 |
0.237 |
0.329 |
| HMC |
0.5 |
0.990 |
0.326 |
0.289 |
| HMC |
0.9 |
3.385 |
0.00159 |
1.482 |
| HMC |
0.95 |
2.186 |
0.0338 |
0.782 |
| HMC |
0.99 |
2.149 |
0.0381 |
1.045 |
| SMC |
0.0 |
-1.278 |
0.207 |
-0.286 |
| SMC |
0.3 |
0.502 |
0.617 |
0.134 |
| SMC |
0.5 |
0.641 |
0.524 |
0.174 |
| SMC |
0.9 |
1.143 |
0.26 |
0.513 |
| SMC |
0.95 |
-0.089 |
0.929 |
-0.025 |
| SMC |
0.99 |
-0.639 |
0.525 |
-0.191 |
| Metro |
0.0 |
3.730 |
0.000532 |
1.409 |
| Metro |
0.3 |
3.103 |
0.00308 |
0.973 |
| Metro |
0.5 |
3.839 |
0.000481 |
2.120 |
| Metro |
0.9 |
3.749 |
0.000768 |
6.406 |
| Metro |
0.95 |
6.325 |
4.37e-07 |
5.376 |
| Metro |
0.99 |
3.898 |
0.000527 |
29.490 |
| DEMetro_Z |
0.0 |
3.631 |
0.000999 |
3.440 |
| DEMetro_Z |
0.3 |
3.474 |
0.00116 |
1.342 |
| DEMetro_Z |
0.5 |
3.883 |
0.00043 |
2.219 |
| DEMetro_Z |
0.9 |
4.712 |
4.21e-05 |
3.261 |
| DEMetro_Z |
0.95 |
4.222 |
0.000151 |
2.189 |
| DEMetro_Z |
0.99 |
3.620 |
0.000842 |
1.718 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-3.489
|
0.00157
|
-0.637
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.487
|
0.0189
|
-0.454
|
| HMC_vs_DEMetro_Z |
0.5
|
-3.101
|
0.00427
|
-0.566
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.026
|
0.052
|
-0.370
|
| HMC_vs_DEMetro_Z |
0.95
|
-2.873
|
0.00753
|
-0.525
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.984
|
0.333
|
-0.180
|
| Metro_vs_SMC |
0.0
|
4.773
|
4.77e-05
|
0.871
|
| Metro_vs_SMC |
0.3
|
2.842
|
0.00813
|
0.519
|
| Metro_vs_SMC |
0.5
|
4.000
|
0.000401
|
0.730
|
| Metro_vs_SMC |
0.9
|
3.251
|
0.00291
|
0.594
|
| Metro_vs_SMC |
0.95
|
6.506
|
4.02e-07
|
1.188
|
| Metro_vs_SMC |
0.99
|
3.905
|
0.000518
|
0.713
|
| Metro_vs_DEMetro_Z |
0.0
|
-2.011
|
0.0537
|
-0.367
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.970
|
0.34
|
-0.177
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.121
|
0.905
|
-0.022
|
| Metro_vs_DEMetro_Z |
0.9
|
1.662
|
0.107
|
0.303
|
| Metro_vs_DEMetro_Z |
0.95
|
3.265
|
0.00281
|
0.596
|
| Metro_vs_DEMetro_Z |
0.99
|
3.616
|
0.00112
|
0.660
|
| HMC_vs_Metro |
0.0
|
-3.909
|
0.000513
|
-0.714
|
| HMC_vs_Metro |
0.3
|
-3.161
|
0.00367
|
-0.577
|
| HMC_vs_Metro |
0.5
|
-3.332
|
0.00236
|
-0.608
|
| HMC_vs_Metro |
0.9
|
-2.964
|
0.00601
|
-0.541
|
| HMC_vs_Metro |
0.95
|
-5.227
|
1.35e-05
|
-0.954
|
| HMC_vs_Metro |
0.99
|
-3.732
|
0.000823
|
-0.681
|
| HMC_vs_SMC |
0.0
|
1.936
|
0.0626
|
0.354
|
| HMC_vs_SMC |
0.3
|
0.883
|
0.385
|
0.161
|
| HMC_vs_SMC |
0.5
|
0.507
|
0.616
|
0.092
|
| HMC_vs_SMC |
0.9
|
1.764
|
0.0882
|
0.322
|
| HMC_vs_SMC |
0.95
|
2.347
|
0.0259
|
0.429
|
| HMC_vs_SMC |
0.99
|
2.362
|
0.0251
|
0.431
|
| DEMetro_Z_vs_SMC |
0.0
|
3.811
|
0.000667
|
0.696
|
| DEMetro_Z_vs_SMC |
0.3
|
3.130
|
0.00396
|
0.571
|
| DEMetro_Z_vs_SMC |
0.5
|
3.421
|
0.00187
|
0.625
|
| DEMetro_Z_vs_SMC |
0.9
|
3.564
|
0.00129
|
0.651
|
| DEMetro_Z_vs_SMC |
0.95
|
3.976
|
0.000427
|
0.726
|
| DEMetro_Z_vs_SMC |
0.99
|
4.494
|
0.000103
|
0.820
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.066 |
0.065 |
0.042 |
0.037 |
| HMC |
0.3 |
0.069 |
0.056 |
0.040 |
0.329 |
| HMC |
0.5 |
0.082 |
0.068 |
0.046 |
0.289 |
| HMC |
0.9 |
0.086 |
0.047 |
0.027 |
1.482 |
| HMC |
0.95 |
0.082 |
0.053 |
0.037 |
0.782 |
| HMC |
0.99 |
0.110 |
0.061 |
0.047 |
1.045 |
| SMC |
0.0 |
0.053 |
0.065 |
0.042 |
-0.286 |
| SMC |
0.3 |
0.061 |
0.056 |
0.040 |
0.134 |
| SMC |
0.5 |
0.076 |
0.068 |
0.046 |
0.174 |
| SMC |
0.9 |
0.061 |
0.047 |
0.027 |
0.513 |
| SMC |
0.95 |
0.052 |
0.053 |
0.037 |
-0.025 |
| SMC |
0.99 |
0.052 |
0.061 |
0.047 |
-0.191 |
| Metro |
0.0 |
0.124 |
0.065 |
0.042 |
1.409 |
| Metro |
0.3 |
0.094 |
0.056 |
0.040 |
0.973 |
| Metro |
0.5 |
0.167 |
0.068 |
0.046 |
2.120 |
| Metro |
0.9 |
0.218 |
0.047 |
0.027 |
6.406 |
| Metro |
0.95 |
0.251 |
0.053 |
0.037 |
5.376 |
| Metro |
0.99 |
1.458 |
0.061 |
0.047 |
29.490 |
| DEMetro_Z |
0.0 |
0.209 |
0.065 |
0.042 |
3.440 |
| DEMetro_Z |
0.3 |
0.109 |
0.056 |
0.040 |
1.342 |
| DEMetro_Z |
0.5 |
0.171 |
0.068 |
0.046 |
2.219 |
| DEMetro_Z |
0.9 |
0.134 |
0.047 |
0.027 |
3.261 |
| DEMetro_Z |
0.95 |
0.134 |
0.053 |
0.037 |
2.189 |
| DEMetro_Z |
0.99 |
0.142 |
0.061 |
0.047 |
1.718 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.900 |
0.372 |
-0.213 |
| HMC |
0.3 |
1.080 |
0.289 |
1.582 |
| HMC |
0.5 |
0.344 |
0.732 |
0.087 |
| HMC |
0.9 |
-0.338 |
0.737 |
-0.078 |
| HMC |
0.95 |
0.588 |
0.559 |
0.163 |
| HMC |
0.99 |
0.240 |
0.811 |
0.073 |
| SMC |
0.0 |
-2.116 |
0.0418 |
-0.402 |
| SMC |
0.3 |
1.040 |
0.307 |
3.162 |
| SMC |
0.5 |
0.471 |
0.639 |
0.119 |
| SMC |
0.9 |
-0.296 |
0.768 |
-0.072 |
| SMC |
0.95 |
-1.327 |
0.191 |
-0.288 |
| SMC |
0.99 |
-1.609 |
0.117 |
-0.308 |
| Metro |
0.0 |
-1.167 |
0.249 |
-0.249 |
| Metro |
0.3 |
0.535 |
0.595 |
0.169 |
| Metro |
0.5 |
0.673 |
0.504 |
0.174 |
| Metro |
0.9 |
0.119 |
0.906 |
0.027 |
| Metro |
0.95 |
-0.372 |
0.711 |
-0.083 |
| Metro |
0.99 |
1.284 |
0.209 |
1.285 |
| DEMetro_Z |
0.0 |
0.431 |
0.669 |
0.182 |
| DEMetro_Z |
0.3 |
0.900 |
0.373 |
0.286 |
| DEMetro_Z |
0.5 |
0.499 |
0.62 |
0.126 |
| DEMetro_Z |
0.9 |
-0.434 |
0.666 |
-0.096 |
| DEMetro_Z |
0.95 |
-0.169 |
0.866 |
-0.041 |
| DEMetro_Z |
0.99 |
-0.825 |
0.415 |
-0.159 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
1.281
|
0.21
|
0.234
|
| HMC_vs_SMC |
0.3
|
-0.469
|
0.642
|
-0.086
|
| HMC_vs_SMC |
0.5
|
-0.522
|
0.606
|
-0.095
|
| HMC_vs_SMC |
0.9
|
-0.039
|
0.969
|
-0.007
|
| HMC_vs_SMC |
0.95
|
2.428
|
0.0216
|
0.443
|
| HMC_vs_SMC |
0.99
|
1.571
|
0.127
|
0.287
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.072
|
0.293
|
-0.196
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.906
|
0.0666
|
-0.348
|
| Metro_vs_DEMetro_Z |
0.5
|
0.651
|
0.52
|
0.119
|
| Metro_vs_DEMetro_Z |
0.9
|
1.219
|
0.233
|
0.223
|
| Metro_vs_DEMetro_Z |
0.95
|
-0.429
|
0.671
|
-0.078
|
| Metro_vs_DEMetro_Z |
0.99
|
1.531
|
0.137
|
0.280
|
| HMC_vs_Metro |
0.0
|
0.200
|
0.843
|
0.037
|
| HMC_vs_Metro |
0.3
|
0.972
|
0.339
|
0.177
|
| HMC_vs_Metro |
0.5
|
-1.229
|
0.229
|
-0.224
|
| HMC_vs_Metro |
0.9
|
-0.816
|
0.421
|
-0.149
|
| HMC_vs_Metro |
0.95
|
1.244
|
0.223
|
0.227
|
| HMC_vs_Metro |
0.99
|
-1.224
|
0.231
|
-0.223
|
| HMC_vs_DEMetro_Z |
0.0
|
-0.944
|
0.353
|
-0.172
|
| HMC_vs_DEMetro_Z |
0.3
|
0.880
|
0.386
|
0.161
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.349
|
0.188
|
-0.246
|
| HMC_vs_DEMetro_Z |
0.9
|
0.203
|
0.841
|
0.037
|
| HMC_vs_DEMetro_Z |
0.95
|
0.985
|
0.333
|
0.180
|
| HMC_vs_DEMetro_Z |
0.99
|
0.929
|
0.36
|
0.170
|
| Metro_vs_SMC |
0.0
|
1.465
|
0.154
|
0.268
|
| Metro_vs_SMC |
0.3
|
-1.001
|
0.325
|
-0.183
|
| Metro_vs_SMC |
0.5
|
0.611
|
0.546
|
0.112
|
| Metro_vs_SMC |
0.9
|
0.643
|
0.526
|
0.117
|
| Metro_vs_SMC |
0.95
|
5.610
|
4.67e-06
|
1.024
|
| Metro_vs_SMC |
0.99
|
1.681
|
0.104
|
0.307
|
| DEMetro_Z_vs_SMC |
0.0
|
1.501
|
0.144
|
0.274
|
| DEMetro_Z_vs_SMC |
0.3
|
-0.965
|
0.343
|
-0.176
|
| DEMetro_Z_vs_SMC |
0.5
|
0.104
|
0.918
|
0.019
|
| DEMetro_Z_vs_SMC |
0.9
|
-0.180
|
0.859
|
-0.033
|
| DEMetro_Z_vs_SMC |
0.95
|
2.664
|
0.0125
|
0.486
|
| DEMetro_Z_vs_SMC |
0.99
|
2.964
|
0.00601
|
0.541
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
6.074 |
9.112 |
14.240 |
-0.213 |
| HMC |
0.3 |
12.569 |
4.697 |
4.977 |
1.582 |
| HMC |
0.5 |
11.918 |
9.883 |
23.480 |
0.087 |
| HMC |
0.9 |
4.735 |
5.328 |
7.624 |
-0.078 |
| HMC |
0.95 |
8.144 |
6.496 |
10.111 |
0.163 |
| HMC |
0.99 |
6.197 |
5.445 |
10.256 |
0.073 |
| SMC |
0.0 |
3.390 |
9.112 |
14.240 |
-0.402 |
| SMC |
0.3 |
20.434 |
4.697 |
4.977 |
3.162 |
| SMC |
0.5 |
12.681 |
9.883 |
23.480 |
0.119 |
| SMC |
0.9 |
4.781 |
5.328 |
7.624 |
-0.072 |
| SMC |
0.95 |
3.584 |
6.496 |
10.111 |
-0.288 |
| SMC |
0.99 |
2.286 |
5.445 |
10.256 |
-0.308 |
| Metro |
0.0 |
5.560 |
9.112 |
14.240 |
-0.249 |
| Metro |
0.3 |
5.537 |
4.697 |
4.977 |
0.169 |
| Metro |
0.5 |
13.964 |
9.883 |
23.480 |
0.174 |
| Metro |
0.9 |
5.534 |
5.328 |
7.624 |
0.027 |
| Metro |
0.95 |
5.660 |
6.496 |
10.111 |
-0.083 |
| Metro |
0.99 |
18.624 |
5.445 |
10.256 |
1.285 |
| DEMetro_Z |
0.0 |
11.710 |
9.112 |
14.240 |
0.182 |
| DEMetro_Z |
0.3 |
6.119 |
4.697 |
4.977 |
0.286 |
| DEMetro_Z |
0.5 |
12.836 |
9.883 |
23.480 |
0.126 |
| DEMetro_Z |
0.9 |
4.597 |
5.328 |
7.624 |
-0.096 |
| DEMetro_Z |
0.95 |
6.079 |
6.496 |
10.111 |
-0.041 |
| DEMetro_Z |
0.99 |
3.810 |
5.445 |
10.256 |
-0.159 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.659 |
0.0105 |
0.885 |
| HMC |
0.3 |
1.647 |
0.11 |
2.041 |
| HMC |
0.5 |
3.316 |
0.00194 |
1.467 |
| HMC |
0.9 |
5.138 |
4.49e-06 |
1.687 |
| HMC |
0.95 |
4.939 |
2.4e-05 |
4.146 |
| HMC |
0.99 |
4.228 |
0.000155 |
2.347 |
| SMC |
0.0 |
-1.215 |
0.23 |
-0.271 |
| SMC |
0.3 |
1.149 |
0.258 |
0.548 |
| SMC |
0.5 |
2.071 |
0.0428 |
0.540 |
| SMC |
0.9 |
0.493 |
0.624 |
0.156 |
| SMC |
0.95 |
0.056 |
0.956 |
0.018 |
| SMC |
0.99 |
0.695 |
0.49 |
0.228 |
| Metro |
0.0 |
3.937 |
0.000424 |
3.447 |
| Metro |
0.3 |
7.021 |
1.09e-08 |
2.759 |
| Metro |
0.5 |
5.508 |
4.4e-06 |
4.334 |
| Metro |
0.9 |
6.616 |
2.11e-07 |
6.411 |
| Metro |
0.95 |
12.351 |
1.6e-13 |
12.155 |
| Metro |
0.99 |
5.137 |
1.73e-05 |
40.023 |
| DEMetro_Z |
0.0 |
4.177 |
0.000235 |
6.062 |
| DEMetro_Z |
0.3 |
8.724 |
1.28e-10 |
4.276 |
| DEMetro_Z |
0.5 |
8.201 |
8.55e-10 |
4.412 |
| DEMetro_Z |
0.9 |
9.383 |
1.31e-11 |
4.300 |
| DEMetro_Z |
0.95 |
4.216 |
0.000215 |
7.501 |
| DEMetro_Z |
0.99 |
8.148 |
6.64e-10 |
3.922 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-1.519
|
0.14
|
-0.277
|
| Metro_vs_DEMetro_Z |
0.3
|
-3.185
|
0.00345
|
-0.581
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.080
|
0.937
|
-0.015
|
| Metro_vs_DEMetro_Z |
0.9
|
2.216
|
0.0347
|
0.404
|
| Metro_vs_DEMetro_Z |
0.95
|
2.124
|
0.0423
|
0.388
|
| Metro_vs_DEMetro_Z |
0.99
|
4.614
|
7.4e-05
|
0.842
|
| DEMetro_Z_vs_SMC |
0.0
|
4.292
|
0.00018
|
0.784
|
| DEMetro_Z_vs_SMC |
0.3
|
6.249
|
8.06e-07
|
1.141
|
| DEMetro_Z_vs_SMC |
0.5
|
7.005
|
1.06e-07
|
1.279
|
| DEMetro_Z_vs_SMC |
0.9
|
8.594
|
1.82e-09
|
1.569
|
| DEMetro_Z_vs_SMC |
0.95
|
4.147
|
0.000268
|
0.757
|
| DEMetro_Z_vs_SMC |
0.99
|
7.570
|
2.41e-08
|
1.382
|
| HMC_vs_DEMetro_Z |
0.0
|
-3.398
|
0.00199
|
-0.620
|
| HMC_vs_DEMetro_Z |
0.3
|
-1.613
|
0.118
|
-0.294
|
| HMC_vs_DEMetro_Z |
0.5
|
-4.845
|
3.91e-05
|
-0.884
|
| HMC_vs_DEMetro_Z |
0.9
|
-4.551
|
8.82e-05
|
-0.831
|
| HMC_vs_DEMetro_Z |
0.95
|
-1.715
|
0.0969
|
-0.313
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.091
|
0.0454
|
-0.382
|
| HMC_vs_Metro |
0.0
|
-2.819
|
0.00859
|
-0.515
|
| HMC_vs_Metro |
0.3
|
-0.641
|
0.526
|
-0.117
|
| HMC_vs_Metro |
0.5
|
-3.308
|
0.00252
|
-0.604
|
| HMC_vs_Metro |
0.9
|
-4.832
|
4.05e-05
|
-0.882
|
| HMC_vs_Metro |
0.95
|
-5.857
|
2.36e-06
|
-1.069
|
| HMC_vs_Metro |
0.99
|
-4.830
|
4.07e-05
|
-0.882
|
| HMC_vs_SMC |
0.0
|
4.600
|
7.69e-05
|
0.840
|
| HMC_vs_SMC |
0.3
|
1.152
|
0.259
|
0.210
|
| HMC_vs_SMC |
0.5
|
2.270
|
0.0308
|
0.414
|
| HMC_vs_SMC |
0.9
|
4.069
|
0.000332
|
0.743
|
| HMC_vs_SMC |
0.95
|
4.669
|
6.36e-05
|
0.852
|
| HMC_vs_SMC |
0.99
|
3.654
|
0.00101
|
0.667
|
| Metro_vs_SMC |
0.0
|
4.327
|
0.000164
|
0.790
|
| Metro_vs_SMC |
0.3
|
3.995
|
0.000406
|
0.729
|
| Metro_vs_SMC |
0.5
|
5.046
|
2.23e-05
|
0.921
|
| Metro_vs_SMC |
0.9
|
6.186
|
9.57e-07
|
1.129
|
| Metro_vs_SMC |
0.95
|
12.614
|
2.67e-13
|
2.303
|
| Metro_vs_SMC |
0.99
|
5.075
|
2.06e-05
|
0.926
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.155 |
0.124 |
0.035 |
0.885 |
| HMC |
0.3 |
0.172 |
0.116 |
0.027 |
2.041 |
| HMC |
0.5 |
0.173 |
0.120 |
0.036 |
1.467 |
| HMC |
0.9 |
0.171 |
0.115 |
0.034 |
1.687 |
| HMC |
0.95 |
0.212 |
0.111 |
0.025 |
4.146 |
| HMC |
0.99 |
0.204 |
0.111 |
0.040 |
2.347 |
| SMC |
0.0 |
0.114 |
0.124 |
0.035 |
-0.271 |
| SMC |
0.3 |
0.131 |
0.116 |
0.027 |
0.548 |
| SMC |
0.5 |
0.139 |
0.120 |
0.036 |
0.540 |
| SMC |
0.9 |
0.120 |
0.115 |
0.034 |
0.156 |
| SMC |
0.95 |
0.111 |
0.111 |
0.025 |
0.018 |
| SMC |
0.99 |
0.120 |
0.111 |
0.040 |
0.228 |
| Metro |
0.0 |
0.244 |
0.124 |
0.035 |
3.447 |
| Metro |
0.3 |
0.191 |
0.116 |
0.027 |
2.759 |
| Metro |
0.5 |
0.277 |
0.120 |
0.036 |
4.334 |
| Metro |
0.9 |
0.330 |
0.115 |
0.034 |
6.411 |
| Metro |
0.95 |
0.409 |
0.111 |
0.025 |
12.155 |
| Metro |
0.99 |
1.694 |
0.111 |
0.040 |
40.023 |
| DEMetro_Z |
0.0 |
0.336 |
0.124 |
0.035 |
6.062 |
| DEMetro_Z |
0.3 |
0.232 |
0.116 |
0.027 |
4.276 |
| DEMetro_Z |
0.5 |
0.280 |
0.120 |
0.036 |
4.412 |
| DEMetro_Z |
0.9 |
0.259 |
0.115 |
0.034 |
4.300 |
| DEMetro_Z |
0.95 |
0.295 |
0.111 |
0.025 |
7.501 |
| DEMetro_Z |
0.99 |
0.266 |
0.111 |
0.040 |
3.922 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
3.640 |
0.000643 |
1.201 |
| HMC |
0.3 |
2.862 |
0.00612 |
0.941 |
| HMC |
0.5 |
2.668 |
0.0116 |
1.724 |
| HMC |
0.9 |
4.027 |
0.00026 |
1.976 |
| HMC |
0.95 |
5.801 |
1.41e-06 |
3.442 |
| HMC |
0.99 |
5.854 |
3.99e-07 |
2.013 |
| SMC |
0.0 |
0.564 |
0.575 |
0.153 |
| SMC |
0.3 |
1.750 |
0.0876 |
0.766 |
| SMC |
0.5 |
1.862 |
0.0686 |
0.632 |
| SMC |
0.9 |
1.892 |
0.0641 |
0.605 |
| SMC |
0.95 |
1.928 |
0.06 |
0.706 |
| SMC |
0.99 |
2.867 |
0.0063 |
1.095 |
| Metro |
0.0 |
9.213 |
2.76e-11 |
4.420 |
| Metro |
0.3 |
7.464 |
5.44e-09 |
3.598 |
| Metro |
0.5 |
8.291 |
1.6e-09 |
6.358 |
| Metro |
0.9 |
13.684 |
1.12e-15 |
7.943 |
| Metro |
0.95 |
12.289 |
3.39e-13 |
19.185 |
| Metro |
0.99 |
10.301 |
3.19e-11 |
40.306 |
| DEMetro_Z |
0.0 |
7.584 |
1.09e-08 |
5.721 |
| DEMetro_Z |
0.3 |
8.617 |
2.47e-10 |
4.588 |
| DEMetro_Z |
0.5 |
9.691 |
1.86e-11 |
5.706 |
| DEMetro_Z |
0.9 |
10.172 |
2.01e-12 |
4.967 |
| DEMetro_Z |
0.95 |
7.462 |
2.06e-08 |
7.323 |
| DEMetro_Z |
0.99 |
7.979 |
6.95e-10 |
3.437 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
7.540
|
2.6e-08
|
1.377
|
| DEMetro_Z_vs_SMC |
0.3
|
5.198
|
1.46e-05
|
0.949
|
| DEMetro_Z_vs_SMC |
0.5
|
7.453
|
3.26e-08
|
1.361
|
| DEMetro_Z_vs_SMC |
0.9
|
7.930
|
9.57e-09
|
1.448
|
| DEMetro_Z_vs_SMC |
0.95
|
6.477
|
4.34e-07
|
1.183
|
| DEMetro_Z_vs_SMC |
0.99
|
4.326
|
0.000164
|
0.790
|
| HMC_vs_Metro |
0.0
|
-5.558
|
5.39e-06
|
-1.015
|
| HMC_vs_Metro |
0.3
|
-5.310
|
1.07e-05
|
-0.970
|
| HMC_vs_Metro |
0.5
|
-4.387
|
0.000139
|
-0.801
|
| HMC_vs_Metro |
0.9
|
-7.959
|
8.89e-09
|
-1.453
|
| HMC_vs_Metro |
0.95
|
-9.189
|
4.34e-10
|
-1.678
|
| HMC_vs_Metro |
0.99
|
-9.856
|
9.16e-11
|
-1.799
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.705
|
0.099
|
-0.311
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.659
|
0.108
|
-0.303
|
| Metro_vs_DEMetro_Z |
0.5
|
0.669
|
0.509
|
0.122
|
| Metro_vs_DEMetro_Z |
0.9
|
3.979
|
0.000424
|
0.726
|
| Metro_vs_DEMetro_Z |
0.95
|
6.561
|
3.46e-07
|
1.198
|
| Metro_vs_DEMetro_Z |
0.99
|
9.283
|
3.47e-10
|
1.695
|
| HMC_vs_SMC |
0.0
|
4.541
|
9.06e-05
|
0.829
|
| HMC_vs_SMC |
0.3
|
0.418
|
0.679
|
0.076
|
| HMC_vs_SMC |
0.5
|
1.662
|
0.107
|
0.303
|
| HMC_vs_SMC |
0.9
|
2.607
|
0.0143
|
0.476
|
| HMC_vs_SMC |
0.95
|
4.387
|
0.000139
|
0.801
|
| HMC_vs_SMC |
0.99
|
1.806
|
0.0813
|
0.330
|
| Metro_vs_SMC |
0.0
|
8.331
|
3.49e-09
|
1.521
|
| Metro_vs_SMC |
0.3
|
4.333
|
0.000161
|
0.791
|
| Metro_vs_SMC |
0.5
|
7.318
|
4.63e-08
|
1.336
|
| Metro_vs_SMC |
0.9
|
10.677
|
1.46e-11
|
1.949
|
| Metro_vs_SMC |
0.95
|
12.304
|
4.92e-13
|
2.246
|
| Metro_vs_SMC |
0.99
|
9.857
|
9.15e-11
|
1.800
|
| HMC_vs_DEMetro_Z |
0.0
|
-5.545
|
5.58e-06
|
-1.012
|
| HMC_vs_DEMetro_Z |
0.3
|
-6.256
|
7.9e-07
|
-1.142
|
| HMC_vs_DEMetro_Z |
0.5
|
-5.287
|
1.14e-05
|
-0.965
|
| HMC_vs_DEMetro_Z |
0.9
|
-4.060
|
0.000339
|
-0.741
|
| HMC_vs_DEMetro_Z |
0.95
|
-3.625
|
0.00109
|
-0.662
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.807
|
0.00884
|
-0.513
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.020 |
0.015 |
0.005 |
1.201 |
| HMC |
0.3 |
0.019 |
0.015 |
0.004 |
0.941 |
| HMC |
0.5 |
0.022 |
0.015 |
0.004 |
1.724 |
| HMC |
0.9 |
0.024 |
0.014 |
0.005 |
1.976 |
| HMC |
0.95 |
0.027 |
0.014 |
0.004 |
3.442 |
| HMC |
0.99 |
0.030 |
0.015 |
0.007 |
2.013 |
| SMC |
0.0 |
0.015 |
0.015 |
0.005 |
0.153 |
| SMC |
0.3 |
0.018 |
0.015 |
0.004 |
0.766 |
| SMC |
0.5 |
0.017 |
0.015 |
0.004 |
0.632 |
| SMC |
0.9 |
0.017 |
0.014 |
0.005 |
0.605 |
| SMC |
0.95 |
0.017 |
0.014 |
0.004 |
0.706 |
| SMC |
0.99 |
0.023 |
0.015 |
0.007 |
1.095 |
| Metro |
0.0 |
0.035 |
0.015 |
0.005 |
4.420 |
| Metro |
0.3 |
0.029 |
0.015 |
0.004 |
3.598 |
| Metro |
0.5 |
0.040 |
0.015 |
0.004 |
6.358 |
| Metro |
0.9 |
0.052 |
0.014 |
0.005 |
7.943 |
| Metro |
0.95 |
0.084 |
0.014 |
0.004 |
19.185 |
| Metro |
0.99 |
0.301 |
0.015 |
0.007 |
40.306 |
| DEMetro_Z |
0.0 |
0.041 |
0.015 |
0.005 |
5.721 |
| DEMetro_Z |
0.3 |
0.034 |
0.015 |
0.004 |
4.588 |
| DEMetro_Z |
0.5 |
0.038 |
0.015 |
0.004 |
5.706 |
| DEMetro_Z |
0.9 |
0.038 |
0.014 |
0.005 |
4.967 |
| DEMetro_Z |
0.95 |
0.041 |
0.014 |
0.004 |
7.323 |
| DEMetro_Z |
0.99 |
0.040 |
0.015 |
0.007 |
3.437 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
0.5
0.9
0.95
0.99
Vary_Correlation_with_high_Multimodality
(Mixture,
correlation,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
7.138 |
7.28e-08 |
31.388 |
| HMC |
0.3 |
7.170 |
6.64e-08 |
26.126 |
| HMC |
0.5 |
7.110 |
7.75e-08 |
25.148 |
| HMC |
0.9 |
7.465 |
2.92e-08 |
17.001 |
| HMC |
0.95 |
8.276 |
3.71e-09 |
21.745 |
| HMC |
0.99 |
6.668 |
2.24e-07 |
10.076 |
| SMC |
0.0 |
1.246 |
0.218 |
0.335 |
| SMC |
0.3 |
-0.539 |
0.592 |
-0.126 |
| SMC |
0.5 |
-1.234 |
0.223 |
-0.278 |
| SMC |
0.9 |
-0.683 |
0.498 |
-0.144 |
| SMC |
0.95 |
-0.845 |
0.402 |
-0.209 |
| SMC |
0.99 |
1.460 |
0.15 |
0.382 |
| Metro |
0.0 |
7.044 |
8.29e-08 |
11.557 |
| Metro |
0.3 |
6.363 |
5.17e-07 |
9.473 |
| Metro |
0.5 |
5.329 |
9.56e-06 |
9.559 |
| Metro |
0.9 |
5.229 |
1.13e-05 |
5.401 |
| Metro |
0.95 |
6.927 |
1.06e-07 |
9.165 |
| Metro |
0.99 |
6.103 |
1.07e-06 |
9.552 |
| DEMetro_Z |
0.0 |
6.243 |
7.68e-07 |
13.316 |
| DEMetro_Z |
0.3 |
6.306 |
6.57e-07 |
15.388 |
| DEMetro_Z |
0.5 |
6.337 |
5.88e-07 |
12.576 |
| DEMetro_Z |
0.9 |
6.605 |
2.82e-07 |
12.854 |
| DEMetro_Z |
0.95 |
6.023 |
1.31e-06 |
8.526 |
| DEMetro_Z |
0.99 |
6.209 |
6.12e-07 |
5.301 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
3.527
|
0.00142
|
0.644
|
| HMC_vs_DEMetro_Z |
0.3
|
2.410
|
0.0225
|
0.440
|
| HMC_vs_DEMetro_Z |
0.5
|
3.209
|
0.00324
|
0.586
|
| HMC_vs_DEMetro_Z |
0.9
|
1.387
|
0.176
|
0.253
|
| HMC_vs_DEMetro_Z |
0.95
|
3.957
|
0.00045
|
0.722
|
| HMC_vs_DEMetro_Z |
0.99
|
2.943
|
0.00634
|
0.537
|
| Metro_vs_SMC |
0.0
|
6.716
|
2.28e-07
|
1.226
|
| Metro_vs_SMC |
0.3
|
6.328
|
6.5e-07
|
1.155
|
| Metro_vs_SMC |
0.5
|
5.442
|
7.42e-06
|
0.994
|
| Metro_vs_SMC |
0.9
|
5.499
|
6.34e-06
|
1.004
|
| Metro_vs_SMC |
0.95
|
6.779
|
1.93e-07
|
1.238
|
| Metro_vs_SMC |
0.99
|
5.776
|
2.95e-06
|
1.054
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.678
|
0.503
|
-0.124
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.786
|
0.0846
|
-0.326
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.186
|
0.245
|
-0.217
|
| Metro_vs_DEMetro_Z |
0.9
|
-3.585
|
0.00122
|
-0.655
|
| Metro_vs_DEMetro_Z |
0.95
|
0.313
|
0.757
|
0.057
|
| Metro_vs_DEMetro_Z |
0.99
|
2.895
|
0.00713
|
0.529
|
| HMC_vs_Metro |
0.0
|
4.070
|
0.00033
|
0.743
|
| HMC_vs_Metro |
0.3
|
4.460
|
0.000113
|
0.814
|
| HMC_vs_Metro |
0.5
|
4.038
|
0.000361
|
0.737
|
| HMC_vs_Metro |
0.9
|
4.784
|
4.62e-05
|
0.873
|
| HMC_vs_Metro |
0.95
|
4.695
|
5.92e-05
|
0.857
|
| HMC_vs_Metro |
0.99
|
0.227
|
0.822
|
0.041
|
| HMC_vs_SMC |
0.0
|
6.965
|
1.17e-07
|
1.272
|
| HMC_vs_SMC |
0.3
|
7.093
|
8.37e-08
|
1.295
|
| HMC_vs_SMC |
0.5
|
7.173
|
6.78e-08
|
1.310
|
| HMC_vs_SMC |
0.9
|
7.545
|
2.57e-08
|
1.377
|
| HMC_vs_SMC |
0.95
|
8.471
|
2.47e-09
|
1.547
|
| HMC_vs_SMC |
0.99
|
6.371
|
5.79e-07
|
1.163
|
| DEMetro_Z_vs_SMC |
0.0
|
6.112
|
1.17e-06
|
1.116
|
| DEMetro_Z_vs_SMC |
0.3
|
6.390
|
5.49e-07
|
1.167
|
| DEMetro_Z_vs_SMC |
0.5
|
6.413
|
5.17e-07
|
1.171
|
| DEMetro_Z_vs_SMC |
0.9
|
6.684
|
2.48e-07
|
1.220
|
| DEMetro_Z_vs_SMC |
0.95
|
6.071
|
1.31e-06
|
1.108
|
| DEMetro_Z_vs_SMC |
0.99
|
5.850
|
2.41e-06
|
1.068
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.110 |
0.052 |
0.034 |
31.388 |
| HMC |
0.3 |
1.005 |
0.054 |
0.036 |
26.126 |
| HMC |
0.5 |
0.942 |
0.051 |
0.035 |
25.148 |
| HMC |
0.9 |
0.409 |
0.030 |
0.022 |
17.001 |
| HMC |
0.95 |
0.352 |
0.023 |
0.015 |
21.745 |
| HMC |
0.99 |
0.133 |
0.018 |
0.011 |
10.076 |
| SMC |
0.0 |
0.063 |
0.052 |
0.034 |
0.335 |
| SMC |
0.3 |
0.049 |
0.054 |
0.036 |
-0.126 |
| SMC |
0.5 |
0.041 |
0.051 |
0.035 |
-0.278 |
| SMC |
0.9 |
0.027 |
0.030 |
0.022 |
-0.144 |
| SMC |
0.95 |
0.020 |
0.023 |
0.015 |
-0.209 |
| SMC |
0.99 |
0.022 |
0.018 |
0.011 |
0.382 |
| Metro |
0.0 |
0.441 |
0.052 |
0.034 |
11.557 |
| Metro |
0.3 |
0.399 |
0.054 |
0.036 |
9.473 |
| Metro |
0.5 |
0.390 |
0.051 |
0.035 |
9.559 |
| Metro |
0.9 |
0.150 |
0.030 |
0.022 |
5.401 |
| Metro |
0.95 |
0.162 |
0.023 |
0.015 |
9.165 |
| Metro |
0.99 |
0.127 |
0.018 |
0.011 |
9.552 |
| DEMetro_Z |
0.0 |
0.501 |
0.052 |
0.034 |
13.316 |
| DEMetro_Z |
0.3 |
0.614 |
0.054 |
0.036 |
15.388 |
| DEMetro_Z |
0.5 |
0.497 |
0.051 |
0.035 |
12.576 |
| DEMetro_Z |
0.9 |
0.316 |
0.030 |
0.022 |
12.854 |
| DEMetro_Z |
0.95 |
0.152 |
0.023 |
0.015 |
8.526 |
| DEMetro_Z |
0.99 |
0.079 |
0.018 |
0.011 |
5.301 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.402 |
0.000133 |
35.278 |
| HMC |
0.3 |
4.585 |
8e-05 |
31.432 |
| HMC |
0.5 |
4.159 |
0.000259 |
24.917 |
| HMC |
0.9 |
3.680 |
0.000938 |
10.492 |
| HMC |
0.95 |
4.161 |
0.000248 |
6.551 |
| HMC |
0.99 |
5.048 |
1.17e-05 |
2.542 |
| SMC |
0.0 |
-1.026 |
0.309 |
-0.245 |
| SMC |
0.3 |
1.087 |
0.282 |
0.301 |
| SMC |
0.5 |
-0.091 |
0.928 |
-0.023 |
| SMC |
0.9 |
1.646 |
0.105 |
0.464 |
| SMC |
0.95 |
-0.820 |
0.416 |
-0.180 |
| SMC |
0.99 |
0.397 |
0.693 |
0.105 |
| Metro |
0.0 |
4.690 |
5.24e-05 |
4.795 |
| Metro |
0.3 |
4.608 |
6.8e-05 |
5.314 |
| Metro |
0.5 |
3.793 |
0.000665 |
4.776 |
| Metro |
0.9 |
7.827 |
6.19e-09 |
6.361 |
| Metro |
0.95 |
6.414 |
2.13e-07 |
3.727 |
| Metro |
0.99 |
6.188 |
7.7e-07 |
7.108 |
| DEMetro_Z |
0.0 |
3.253 |
0.00286 |
6.842 |
| DEMetro_Z |
0.3 |
3.358 |
0.0022 |
12.056 |
| DEMetro_Z |
0.5 |
3.153 |
0.00371 |
7.114 |
| DEMetro_Z |
0.9 |
4.414 |
0.000125 |
8.497 |
| DEMetro_Z |
0.95 |
4.201 |
0.000168 |
2.344 |
| DEMetro_Z |
0.99 |
5.581 |
2.66e-06 |
3.210 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
4.426
|
0.000125
|
0.808
|
| HMC_vs_SMC |
0.3
|
4.513
|
9.8e-05
|
0.824
|
| HMC_vs_SMC |
0.5
|
4.160
|
0.000258
|
0.760
|
| HMC_vs_SMC |
0.9
|
3.472
|
0.00164
|
0.634
|
| HMC_vs_SMC |
0.95
|
4.270
|
0.000191
|
0.780
|
| HMC_vs_SMC |
0.99
|
4.917
|
3.2e-05
|
0.898
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.895
|
0.378
|
-0.163
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.680
|
0.104
|
-0.307
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.989
|
0.331
|
-0.181
|
| Metro_vs_DEMetro_Z |
0.9
|
-1.022
|
0.315
|
-0.187
|
| Metro_vs_DEMetro_Z |
0.95
|
1.909
|
0.0662
|
0.349
|
| Metro_vs_DEMetro_Z |
0.99
|
3.859
|
0.000587
|
0.704
|
| HMC_vs_Metro |
0.0
|
3.676
|
0.000957
|
0.671
|
| HMC_vs_Metro |
0.3
|
3.799
|
0.000688
|
0.694
|
| HMC_vs_Metro |
0.5
|
3.231
|
0.00306
|
0.590
|
| HMC_vs_Metro |
0.9
|
1.380
|
0.178
|
0.252
|
| HMC_vs_Metro |
0.95
|
1.710
|
0.0979
|
0.312
|
| HMC_vs_Metro |
0.99
|
-3.804
|
0.000679
|
-0.695
|
| HMC_vs_DEMetro_Z |
0.0
|
3.356
|
0.00222
|
0.613
|
| HMC_vs_DEMetro_Z |
0.3
|
2.458
|
0.0202
|
0.449
|
| HMC_vs_DEMetro_Z |
0.5
|
2.761
|
0.0099
|
0.504
|
| HMC_vs_DEMetro_Z |
0.9
|
0.529
|
0.601
|
0.097
|
| HMC_vs_DEMetro_Z |
0.95
|
2.409
|
0.0226
|
0.440
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.025
|
0.314
|
-0.187
|
| Metro_vs_SMC |
0.0
|
4.712
|
5.65e-05
|
0.860
|
| Metro_vs_SMC |
0.3
|
4.425
|
0.000125
|
0.808
|
| Metro_vs_SMC |
0.5
|
3.826
|
0.000641
|
0.698
|
| Metro_vs_SMC |
0.9
|
7.303
|
4.82e-08
|
1.333
|
| Metro_vs_SMC |
0.95
|
6.892
|
1.42e-07
|
1.258
|
| Metro_vs_SMC |
0.99
|
6.373
|
5.76e-07
|
1.164
|
| DEMetro_Z_vs_SMC |
0.0
|
3.446
|
0.00175
|
0.629
|
| DEMetro_Z_vs_SMC |
0.3
|
3.265
|
0.00281
|
0.596
|
| DEMetro_Z_vs_SMC |
0.5
|
3.173
|
0.00355
|
0.579
|
| DEMetro_Z_vs_SMC |
0.9
|
4.118
|
0.00029
|
0.752
|
| DEMetro_Z_vs_SMC |
0.95
|
4.605
|
7.59e-05
|
0.841
|
| DEMetro_Z_vs_SMC |
0.99
|
5.684
|
3.8e-06
|
1.038
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
2.677 |
0.108 |
0.073 |
35.278 |
| HMC |
0.3 |
2.134 |
0.096 |
0.065 |
31.432 |
| HMC |
0.5 |
1.946 |
0.100 |
0.074 |
24.917 |
| HMC |
0.9 |
0.331 |
0.049 |
0.027 |
10.492 |
| HMC |
0.95 |
0.247 |
0.047 |
0.030 |
6.551 |
| HMC |
0.99 |
0.071 |
0.028 |
0.017 |
2.542 |
| SMC |
0.0 |
0.091 |
0.108 |
0.073 |
-0.245 |
| SMC |
0.3 |
0.116 |
0.096 |
0.065 |
0.301 |
| SMC |
0.5 |
0.099 |
0.100 |
0.074 |
-0.023 |
| SMC |
0.9 |
0.061 |
0.049 |
0.027 |
0.464 |
| SMC |
0.95 |
0.042 |
0.047 |
0.030 |
-0.180 |
| SMC |
0.99 |
0.030 |
0.028 |
0.017 |
0.105 |
| Metro |
0.0 |
0.458 |
0.108 |
0.073 |
4.795 |
| Metro |
0.3 |
0.441 |
0.096 |
0.065 |
5.314 |
| Metro |
0.5 |
0.454 |
0.100 |
0.074 |
4.776 |
| Metro |
0.9 |
0.220 |
0.049 |
0.027 |
6.361 |
| Metro |
0.95 |
0.161 |
0.047 |
0.030 |
3.727 |
| Metro |
0.99 |
0.147 |
0.028 |
0.017 |
7.108 |
| DEMetro_Z |
0.0 |
0.607 |
0.108 |
0.073 |
6.842 |
| DEMetro_Z |
0.3 |
0.878 |
0.096 |
0.065 |
12.056 |
| DEMetro_Z |
0.5 |
0.627 |
0.100 |
0.074 |
7.114 |
| DEMetro_Z |
0.9 |
0.278 |
0.049 |
0.027 |
8.497 |
| DEMetro_Z |
0.95 |
0.119 |
0.047 |
0.030 |
2.344 |
| DEMetro_Z |
0.99 |
0.082 |
0.028 |
0.017 |
3.210 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
6.950 |
1.21e-07 |
37.188 |
| HMC |
0.3 |
7.031 |
9.68e-08 |
31.100 |
| HMC |
0.5 |
7.012 |
1.02e-07 |
30.947 |
| HMC |
0.9 |
7.356 |
3.96e-08 |
19.733 |
| HMC |
0.95 |
7.971 |
8.27e-09 |
26.975 |
| HMC |
0.99 |
7.139 |
6.6e-08 |
12.901 |
| SMC |
0.0 |
1.263 |
0.212 |
0.348 |
| SMC |
0.3 |
-0.556 |
0.581 |
-0.125 |
| SMC |
0.5 |
-1.379 |
0.174 |
-0.306 |
| SMC |
0.9 |
-0.907 |
0.369 |
-0.188 |
| SMC |
0.95 |
-0.187 |
0.852 |
-0.045 |
| SMC |
0.99 |
1.287 |
0.203 |
0.345 |
| Metro |
0.0 |
7.065 |
8.11e-08 |
13.329 |
| Metro |
0.3 |
6.541 |
3.26e-07 |
10.841 |
| Metro |
0.5 |
5.303 |
1.05e-05 |
11.675 |
| Metro |
0.9 |
6.420 |
3.93e-07 |
7.031 |
| Metro |
0.95 |
7.681 |
1.52e-08 |
12.258 |
| Metro |
0.99 |
8.039 |
6.34e-09 |
15.257 |
| DEMetro_Z |
0.0 |
6.336 |
6.06e-07 |
15.762 |
| DEMetro_Z |
0.3 |
6.410 |
5e-07 |
17.545 |
| DEMetro_Z |
0.5 |
6.337 |
6.04e-07 |
15.416 |
| DEMetro_Z |
0.9 |
6.978 |
1.04e-07 |
14.535 |
| DEMetro_Z |
0.95 |
6.220 |
8e-07 |
11.225 |
| DEMetro_Z |
0.99 |
7.782 |
9.31e-09 |
8.289 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-0.808
|
0.426
|
-0.147
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.806
|
0.0813
|
-0.330
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.210
|
0.236
|
-0.221
|
| Metro_vs_DEMetro_Z |
0.9
|
-3.325
|
0.00241
|
-0.607
|
| Metro_vs_DEMetro_Z |
0.95
|
0.422
|
0.676
|
0.077
|
| Metro_vs_DEMetro_Z |
0.99
|
3.621
|
0.00111
|
0.661
|
| DEMetro_Z_vs_SMC |
0.0
|
6.274
|
7.53e-07
|
1.145
|
| DEMetro_Z_vs_SMC |
0.3
|
6.481
|
4.29e-07
|
1.183
|
| DEMetro_Z_vs_SMC |
0.5
|
6.425
|
4.99e-07
|
1.173
|
| DEMetro_Z_vs_SMC |
0.9
|
7.008
|
1.05e-07
|
1.279
|
| DEMetro_Z_vs_SMC |
0.95
|
6.204
|
9.13e-07
|
1.133
|
| DEMetro_Z_vs_SMC |
0.99
|
7.734
|
1.58e-08
|
1.412
|
| HMC_vs_DEMetro_Z |
0.0
|
3.475
|
0.00163
|
0.635
|
| HMC_vs_DEMetro_Z |
0.3
|
2.584
|
0.0151
|
0.472
|
| HMC_vs_DEMetro_Z |
0.5
|
3.138
|
0.00389
|
0.573
|
| HMC_vs_DEMetro_Z |
0.9
|
1.516
|
0.14
|
0.277
|
| HMC_vs_DEMetro_Z |
0.95
|
3.633
|
0.00107
|
0.663
|
| HMC_vs_DEMetro_Z |
0.99
|
2.308
|
0.0283
|
0.421
|
| HMC_vs_Metro |
0.0
|
4.071
|
0.00033
|
0.743
|
| HMC_vs_Metro |
0.3
|
4.503
|
0.000101
|
0.822
|
| HMC_vs_Metro |
0.5
|
4.072
|
0.000329
|
0.744
|
| HMC_vs_Metro |
0.9
|
4.493
|
0.000103
|
0.820
|
| HMC_vs_Metro |
0.95
|
4.263
|
0.000195
|
0.778
|
| HMC_vs_Metro |
0.99
|
-0.822
|
0.418
|
-0.150
|
| HMC_vs_SMC |
0.0
|
6.802
|
1.81e-07
|
1.242
|
| HMC_vs_SMC |
0.3
|
6.962
|
1.18e-07
|
1.271
|
| HMC_vs_SMC |
0.5
|
7.073
|
8.82e-08
|
1.291
|
| HMC_vs_SMC |
0.9
|
7.429
|
3.47e-08
|
1.356
|
| HMC_vs_SMC |
0.95
|
8.031
|
7.41e-09
|
1.466
|
| HMC_vs_SMC |
0.99
|
6.956
|
1.2e-07
|
1.270
|
| Metro_vs_SMC |
0.0
|
6.764
|
2.01e-07
|
1.235
|
| Metro_vs_SMC |
0.3
|
6.524
|
3.82e-07
|
1.191
|
| Metro_vs_SMC |
0.5
|
5.392
|
8.54e-06
|
0.984
|
| Metro_vs_SMC |
0.9
|
6.758
|
2.04e-07
|
1.234
|
| Metro_vs_SMC |
0.95
|
7.430
|
3.46e-08
|
1.357
|
| Metro_vs_SMC |
0.99
|
7.763
|
1.46e-08
|
1.417
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.023 |
0.063 |
0.026 |
37.188 |
| HMC |
0.3 |
0.935 |
0.064 |
0.028 |
31.100 |
| HMC |
0.5 |
0.860 |
0.061 |
0.026 |
30.947 |
| HMC |
0.9 |
0.382 |
0.041 |
0.017 |
19.733 |
| HMC |
0.95 |
0.317 |
0.034 |
0.010 |
26.975 |
| HMC |
0.99 |
0.124 |
0.027 |
0.008 |
12.901 |
| SMC |
0.0 |
0.072 |
0.063 |
0.026 |
0.348 |
| SMC |
0.3 |
0.060 |
0.064 |
0.028 |
-0.125 |
| SMC |
0.5 |
0.053 |
0.061 |
0.026 |
-0.306 |
| SMC |
0.9 |
0.037 |
0.041 |
0.017 |
-0.188 |
| SMC |
0.95 |
0.033 |
0.034 |
0.010 |
-0.045 |
| SMC |
0.99 |
0.029 |
0.027 |
0.008 |
0.345 |
| Metro |
0.0 |
0.407 |
0.063 |
0.026 |
13.329 |
| Metro |
0.3 |
0.368 |
0.064 |
0.028 |
10.841 |
| Metro |
0.5 |
0.362 |
0.061 |
0.026 |
11.675 |
| Metro |
0.9 |
0.162 |
0.041 |
0.017 |
7.031 |
| Metro |
0.95 |
0.162 |
0.034 |
0.010 |
12.258 |
| Metro |
0.99 |
0.142 |
0.027 |
0.008 |
15.257 |
| DEMetro_Z |
0.0 |
0.470 |
0.063 |
0.026 |
15.762 |
| DEMetro_Z |
0.3 |
0.556 |
0.064 |
0.028 |
17.545 |
| DEMetro_Z |
0.5 |
0.459 |
0.061 |
0.026 |
15.416 |
| DEMetro_Z |
0.9 |
0.292 |
0.041 |
0.017 |
14.535 |
| DEMetro_Z |
0.95 |
0.151 |
0.034 |
0.010 |
11.225 |
| DEMetro_Z |
0.99 |
0.089 |
0.027 |
0.008 |
8.289 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
6.986 |
1.09e-07 |
36.428 |
| HMC |
0.3 |
7.094 |
8.17e-08 |
29.091 |
| HMC |
0.5 |
7.034 |
9.53e-08 |
26.839 |
| HMC |
0.9 |
7.587 |
2.15e-08 |
19.059 |
| HMC |
0.95 |
8.138 |
5.35e-09 |
24.242 |
| HMC |
0.99 |
7.024 |
9.05e-08 |
13.239 |
| SMC |
0.0 |
0.965 |
0.339 |
0.262 |
| SMC |
0.3 |
-0.288 |
0.775 |
-0.066 |
| SMC |
0.5 |
-1.427 |
0.16 |
-0.307 |
| SMC |
0.9 |
-0.689 |
0.494 |
-0.140 |
| SMC |
0.95 |
-0.382 |
0.704 |
-0.087 |
| SMC |
0.99 |
1.155 |
0.253 |
0.302 |
| Metro |
0.0 |
6.968 |
1.05e-07 |
12.854 |
| Metro |
0.3 |
6.442 |
4.24e-07 |
10.419 |
| Metro |
0.5 |
5.441 |
6.98e-06 |
9.826 |
| Metro |
0.9 |
6.639 |
1.94e-07 |
6.268 |
| Metro |
0.95 |
8.122 |
4.1e-09 |
9.518 |
| Metro |
0.99 |
8.228 |
3.67e-09 |
12.917 |
| DEMetro_Z |
0.0 |
5.966 |
1.68e-06 |
15.121 |
| DEMetro_Z |
0.3 |
6.211 |
8.62e-07 |
17.043 |
| DEMetro_Z |
0.5 |
6.074 |
1.23e-06 |
13.436 |
| DEMetro_Z |
0.9 |
6.640 |
2.61e-07 |
14.557 |
| DEMetro_Z |
0.95 |
6.305 |
6.11e-07 |
9.685 |
| DEMetro_Z |
0.99 |
8.259 |
2.37e-09 |
7.876 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
5.939
|
1.89e-06
|
1.084
|
| DEMetro_Z_vs_SMC |
0.3
|
6.268
|
7.66e-07
|
1.144
|
| DEMetro_Z_vs_SMC |
0.5
|
6.178
|
9.79e-07
|
1.128
|
| DEMetro_Z_vs_SMC |
0.9
|
6.662
|
2.64e-07
|
1.216
|
| DEMetro_Z_vs_SMC |
0.95
|
6.339
|
6.31e-07
|
1.157
|
| DEMetro_Z_vs_SMC |
0.99
|
8.166
|
5.28e-09
|
1.491
|
| HMC_vs_Metro |
0.0
|
4.091
|
0.000312
|
0.747
|
| HMC_vs_Metro |
0.3
|
4.476
|
0.000108
|
0.817
|
| HMC_vs_Metro |
0.5
|
4.123
|
0.000286
|
0.753
|
| HMC_vs_Metro |
0.9
|
5.057
|
2.17e-05
|
0.923
|
| HMC_vs_Metro |
0.95
|
4.925
|
3.13e-05
|
0.899
|
| HMC_vs_Metro |
0.99
|
0.125
|
0.902
|
0.023
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.742
|
0.464
|
-0.135
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.795
|
0.083
|
-0.328
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.356
|
0.185
|
-0.248
|
| Metro_vs_DEMetro_Z |
0.9
|
-3.530
|
0.00141
|
-0.644
|
| Metro_vs_DEMetro_Z |
0.95
|
-0.087
|
0.931
|
-0.016
|
| Metro_vs_DEMetro_Z |
0.99
|
3.113
|
0.00414
|
0.568
|
| HMC_vs_SMC |
0.0
|
6.855
|
1.57e-07
|
1.252
|
| HMC_vs_SMC |
0.3
|
7.007
|
1.05e-07
|
1.279
|
| HMC_vs_SMC |
0.5
|
7.109
|
8.01e-08
|
1.298
|
| HMC_vs_SMC |
0.9
|
7.626
|
2.08e-08
|
1.392
|
| HMC_vs_SMC |
0.95
|
8.240
|
4.38e-09
|
1.504
|
| HMC_vs_SMC |
0.99
|
6.880
|
1.47e-07
|
1.256
|
| Metro_vs_SMC |
0.0
|
6.714
|
2.29e-07
|
1.226
|
| Metro_vs_SMC |
0.3
|
6.368
|
5.83e-07
|
1.163
|
| Metro_vs_SMC |
0.5
|
5.575
|
5.14e-06
|
1.018
|
| Metro_vs_SMC |
0.9
|
6.974
|
1.15e-07
|
1.273
|
| Metro_vs_SMC |
0.95
|
8.011
|
7.79e-09
|
1.463
|
| Metro_vs_SMC |
0.99
|
8.084
|
6.48e-09
|
1.476
|
| HMC_vs_DEMetro_Z |
0.0
|
3.509
|
0.00149
|
0.641
|
| HMC_vs_DEMetro_Z |
0.3
|
2.396
|
0.0232
|
0.437
|
| HMC_vs_DEMetro_Z |
0.5
|
3.142
|
0.00385
|
0.574
|
| HMC_vs_DEMetro_Z |
0.9
|
1.339
|
0.191
|
0.244
|
| HMC_vs_DEMetro_Z |
0.95
|
3.908
|
0.000514
|
0.713
|
| HMC_vs_DEMetro_Z |
0.99
|
2.664
|
0.0125
|
0.486
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.243 |
0.013 |
0.006 |
36.428 |
| HMC |
0.3 |
0.230 |
0.013 |
0.007 |
29.091 |
| HMC |
0.5 |
0.227 |
0.013 |
0.008 |
26.839 |
| HMC |
0.9 |
0.149 |
0.013 |
0.007 |
19.059 |
| HMC |
0.95 |
0.154 |
0.013 |
0.006 |
24.242 |
| HMC |
0.99 |
0.078 |
0.013 |
0.005 |
13.239 |
| SMC |
0.0 |
0.014 |
0.013 |
0.006 |
0.262 |
| SMC |
0.3 |
0.012 |
0.013 |
0.007 |
-0.066 |
| SMC |
0.5 |
0.011 |
0.013 |
0.008 |
-0.307 |
| SMC |
0.9 |
0.012 |
0.013 |
0.007 |
-0.140 |
| SMC |
0.95 |
0.013 |
0.013 |
0.006 |
-0.087 |
| SMC |
0.99 |
0.015 |
0.013 |
0.005 |
0.302 |
| Metro |
0.0 |
0.094 |
0.013 |
0.006 |
12.854 |
| Metro |
0.3 |
0.091 |
0.013 |
0.007 |
10.419 |
| Metro |
0.5 |
0.092 |
0.013 |
0.008 |
9.826 |
| Metro |
0.9 |
0.058 |
0.013 |
0.007 |
6.268 |
| Metro |
0.95 |
0.068 |
0.013 |
0.006 |
9.518 |
| Metro |
0.99 |
0.076 |
0.013 |
0.005 |
12.917 |
| DEMetro_Z |
0.0 |
0.108 |
0.013 |
0.006 |
15.121 |
| DEMetro_Z |
0.3 |
0.140 |
0.013 |
0.007 |
17.043 |
| DEMetro_Z |
0.5 |
0.121 |
0.013 |
0.008 |
13.436 |
| DEMetro_Z |
0.9 |
0.117 |
0.013 |
0.007 |
14.557 |
| DEMetro_Z |
0.95 |
0.069 |
0.013 |
0.006 |
9.685 |
| DEMetro_Z |
0.99 |
0.052 |
0.013 |
0.005 |
7.876 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
11.346 |
3.37e-12 |
57.460 |
| HMC |
0.3 |
12.909 |
1.42e-13 |
53.861 |
| HMC |
0.5 |
7.731 |
1.56e-08 |
37.836 |
| HMC |
0.9 |
7.976 |
8.11e-09 |
24.837 |
| HMC |
0.95 |
10.695 |
1.31e-11 |
35.737 |
| HMC |
0.99 |
8.668 |
1.21e-09 |
13.511 |
| SMC |
0.0 |
0.426 |
0.671 |
0.111 |
| SMC |
0.3 |
-0.311 |
0.757 |
-0.075 |
| SMC |
0.5 |
-1.215 |
0.23 |
-0.269 |
| SMC |
0.9 |
1.001 |
0.321 |
0.241 |
| SMC |
0.95 |
-0.985 |
0.329 |
-0.256 |
| SMC |
0.99 |
0.626 |
0.534 |
0.154 |
| Metro |
0.0 |
5.766 |
2.94e-06 |
16.036 |
| Metro |
0.3 |
6.441 |
4.35e-07 |
11.487 |
| Metro |
0.5 |
5.595 |
4.49e-06 |
9.327 |
| Metro |
0.9 |
6.169 |
8.32e-07 |
7.516 |
| Metro |
0.95 |
9.405 |
9.9e-11 |
7.719 |
| Metro |
0.99 |
4.310 |
0.000166 |
8.245 |
| DEMetro_Z |
0.0 |
4.539 |
8.86e-05 |
9.585 |
| DEMetro_Z |
0.3 |
3.104 |
0.00419 |
6.288 |
| DEMetro_Z |
0.5 |
3.141 |
0.00383 |
7.865 |
| DEMetro_Z |
0.9 |
3.333 |
0.00234 |
8.315 |
| DEMetro_Z |
0.95 |
3.818 |
0.000641 |
7.938 |
| DEMetro_Z |
0.99 |
4.295 |
0.000158 |
4.043 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
8.485
|
2.38e-09
|
1.549
|
| HMC_vs_DEMetro_Z |
0.3
|
10.849
|
1.01e-11
|
1.981
|
| HMC_vs_DEMetro_Z |
0.5
|
5.225
|
1.36e-05
|
0.954
|
| HMC_vs_DEMetro_Z |
0.9
|
4.131
|
0.00028
|
0.754
|
| HMC_vs_DEMetro_Z |
0.95
|
6.603
|
3.09e-07
|
1.206
|
| HMC_vs_DEMetro_Z |
0.99
|
5.725
|
3.39e-06
|
1.045
|
| Metro_vs_SMC |
0.0
|
5.658
|
4.09e-06
|
1.033
|
| Metro_vs_SMC |
0.3
|
6.559
|
3.48e-07
|
1.197
|
| Metro_vs_SMC |
0.5
|
5.733
|
3.32e-06
|
1.047
|
| Metro_vs_SMC |
0.9
|
5.886
|
2.18e-06
|
1.075
|
| Metro_vs_SMC |
0.95
|
9.609
|
1.62e-10
|
1.754
|
| Metro_vs_SMC |
0.99
|
4.346
|
0.000155
|
0.794
|
| Metro_vs_DEMetro_Z |
0.0
|
2.101
|
0.0444
|
0.384
|
| Metro_vs_DEMetro_Z |
0.3
|
1.824
|
0.0785
|
0.333
|
| Metro_vs_DEMetro_Z |
0.5
|
0.477
|
0.637
|
0.087
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.268
|
0.79
|
-0.049
|
| Metro_vs_DEMetro_Z |
0.95
|
-0.099
|
0.922
|
-0.018
|
| Metro_vs_DEMetro_Z |
0.99
|
1.928
|
0.0637
|
0.352
|
| HMC_vs_Metro |
0.0
|
7.463
|
3.17e-08
|
1.363
|
| HMC_vs_Metro |
0.3
|
8.870
|
9.32e-10
|
1.619
|
| HMC_vs_Metro |
0.5
|
5.276
|
1.18e-05
|
0.963
|
| HMC_vs_Metro |
0.9
|
4.718
|
5.56e-05
|
0.861
|
| HMC_vs_Metro |
0.95
|
7.865
|
1.13e-08
|
1.436
|
| HMC_vs_Metro |
0.99
|
2.702
|
0.0114
|
0.493
|
| HMC_vs_SMC |
0.0
|
11.274
|
4.06e-12
|
2.058
|
| HMC_vs_SMC |
0.3
|
12.985
|
1.3e-13
|
2.371
|
| HMC_vs_SMC |
0.5
|
7.832
|
1.23e-08
|
1.430
|
| HMC_vs_SMC |
0.9
|
7.911
|
1e-08
|
1.444
|
| HMC_vs_SMC |
0.95
|
10.704
|
1.38e-11
|
1.954
|
| HMC_vs_SMC |
0.99
|
8.429
|
2.74e-09
|
1.539
|
| DEMetro_Z_vs_SMC |
0.0
|
4.430
|
0.000123
|
0.809
|
| DEMetro_Z_vs_SMC |
0.3
|
3.219
|
0.00316
|
0.588
|
| DEMetro_Z_vs_SMC |
0.5
|
3.234
|
0.00304
|
0.590
|
| DEMetro_Z_vs_SMC |
0.9
|
3.280
|
0.0027
|
0.599
|
| DEMetro_Z_vs_SMC |
0.95
|
3.870
|
0.000569
|
0.707
|
| DEMetro_Z_vs_SMC |
0.99
|
4.052
|
0.000348
|
0.740
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.988 |
0.052 |
0.034 |
57.460 |
| HMC |
0.3 |
2.015 |
0.054 |
0.036 |
53.861 |
| HMC |
0.5 |
1.392 |
0.051 |
0.035 |
37.836 |
| HMC |
0.9 |
0.583 |
0.030 |
0.022 |
24.837 |
| HMC |
0.95 |
0.563 |
0.023 |
0.015 |
35.737 |
| HMC |
0.99 |
0.172 |
0.018 |
0.011 |
13.511 |
| SMC |
0.0 |
0.056 |
0.052 |
0.034 |
0.111 |
| SMC |
0.3 |
0.051 |
0.054 |
0.036 |
-0.075 |
| SMC |
0.5 |
0.041 |
0.051 |
0.035 |
-0.269 |
| SMC |
0.9 |
0.035 |
0.030 |
0.022 |
0.241 |
| SMC |
0.95 |
0.020 |
0.023 |
0.015 |
-0.256 |
| SMC |
0.99 |
0.020 |
0.018 |
0.011 |
0.154 |
| Metro |
0.0 |
0.592 |
0.052 |
0.034 |
16.036 |
| Metro |
0.3 |
0.472 |
0.054 |
0.036 |
11.487 |
| Metro |
0.5 |
0.381 |
0.051 |
0.035 |
9.327 |
| Metro |
0.9 |
0.197 |
0.030 |
0.022 |
7.516 |
| Metro |
0.95 |
0.140 |
0.023 |
0.015 |
7.719 |
| Metro |
0.99 |
0.112 |
0.018 |
0.011 |
8.245 |
| DEMetro_Z |
0.0 |
0.375 |
0.052 |
0.034 |
9.585 |
| DEMetro_Z |
0.3 |
0.283 |
0.054 |
0.036 |
6.288 |
| DEMetro_Z |
0.5 |
0.330 |
0.051 |
0.035 |
7.865 |
| DEMetro_Z |
0.9 |
0.215 |
0.030 |
0.022 |
8.315 |
| DEMetro_Z |
0.95 |
0.143 |
0.023 |
0.015 |
7.938 |
| DEMetro_Z |
0.99 |
0.064 |
0.018 |
0.011 |
4.043 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
8.163 |
5.29e-09 |
91.927 |
| HMC |
0.3 |
9.313 |
3.22e-10 |
100.809 |
| HMC |
0.5 |
6.142 |
1.07e-06 |
52.283 |
| HMC |
0.9 |
4.830 |
4.05e-05 |
23.475 |
| HMC |
0.95 |
6.569 |
3.21e-07 |
15.943 |
| HMC |
0.99 |
6.065 |
6.73e-07 |
3.754 |
| SMC |
0.0 |
0.153 |
0.879 |
0.044 |
| SMC |
0.3 |
0.814 |
0.419 |
0.220 |
| SMC |
0.5 |
-0.522 |
0.604 |
-0.127 |
| SMC |
0.9 |
0.864 |
0.391 |
0.271 |
| SMC |
0.95 |
0.261 |
0.795 |
0.063 |
| SMC |
0.99 |
0.365 |
0.717 |
0.098 |
| Metro |
0.0 |
2.987 |
0.00566 |
11.064 |
| Metro |
0.3 |
4.636 |
6.64e-05 |
7.847 |
| Metro |
0.5 |
3.675 |
0.000911 |
4.339 |
| Metro |
0.9 |
6.941 |
8.98e-08 |
7.240 |
| Metro |
0.95 |
6.204 |
5.42e-07 |
4.539 |
| Metro |
0.99 |
7.109 |
5.48e-08 |
7.114 |
| DEMetro_Z |
0.0 |
3.253 |
0.00284 |
5.195 |
| DEMetro_Z |
0.3 |
2.467 |
0.0197 |
6.386 |
| DEMetro_Z |
0.5 |
1.851 |
0.0743 |
6.836 |
| DEMetro_Z |
0.9 |
2.672 |
0.0122 |
9.034 |
| DEMetro_Z |
0.95 |
2.761 |
0.00969 |
3.310 |
| DEMetro_Z |
0.99 |
5.435 |
3.59e-06 |
2.788 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
8.158
|
5.38e-09
|
1.489
|
| HMC_vs_SMC |
0.3
|
9.283
|
3.47e-10
|
1.695
|
| HMC_vs_SMC |
0.5
|
6.148
|
1.06e-06
|
1.122
|
| HMC_vs_SMC |
0.9
|
4.787
|
4.58e-05
|
0.874
|
| HMC_vs_SMC |
0.95
|
6.622
|
2.94e-07
|
1.209
|
| HMC_vs_SMC |
0.99
|
5.692
|
3.72e-06
|
1.039
|
| Metro_vs_DEMetro_Z |
0.0
|
1.576
|
0.126
|
0.288
|
| Metro_vs_DEMetro_Z |
0.3
|
0.480
|
0.635
|
0.088
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.628
|
0.535
|
-0.115
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.483
|
0.632
|
-0.088
|
| Metro_vs_DEMetro_Z |
0.95
|
0.792
|
0.435
|
0.145
|
| Metro_vs_DEMetro_Z |
0.99
|
4.006
|
0.000394
|
0.731
|
| HMC_vs_Metro |
0.0
|
7.098
|
8.25e-08
|
1.296
|
| HMC_vs_Metro |
0.3
|
8.246
|
4.32e-09
|
1.506
|
| HMC_vs_Metro |
0.5
|
5.524
|
5.93e-06
|
1.008
|
| HMC_vs_Metro |
0.9
|
3.491
|
0.00156
|
0.637
|
| HMC_vs_Metro |
0.95
|
4.634
|
7e-05
|
0.846
|
| HMC_vs_Metro |
0.99
|
-2.570
|
0.0156
|
-0.469
|
| HMC_vs_DEMetro_Z |
0.0
|
7.446
|
3.32e-08
|
1.359
|
| HMC_vs_DEMetro_Z |
0.3
|
8.622
|
1.7e-09
|
1.574
|
| HMC_vs_DEMetro_Z |
0.5
|
4.591
|
7.89e-05
|
0.838
|
| HMC_vs_DEMetro_Z |
0.9
|
2.465
|
0.0198
|
0.450
|
| HMC_vs_DEMetro_Z |
0.95
|
4.330
|
0.000162
|
0.791
|
| HMC_vs_DEMetro_Z |
0.99
|
1.180
|
0.247
|
0.215
|
| Metro_vs_SMC |
0.0
|
2.974
|
0.00587
|
0.543
|
| Metro_vs_SMC |
0.3
|
4.508
|
9.93e-05
|
0.823
|
| Metro_vs_SMC |
0.5
|
3.733
|
0.000821
|
0.682
|
| Metro_vs_SMC |
0.9
|
6.463
|
4.52e-07
|
1.180
|
| Metro_vs_SMC |
0.95
|
6.458
|
4.57e-07
|
1.179
|
| Metro_vs_SMC |
0.99
|
7.098
|
8.25e-08
|
1.296
|
| DEMetro_Z_vs_SMC |
0.0
|
3.268
|
0.00279
|
0.597
|
| DEMetro_Z_vs_SMC |
0.3
|
2.333
|
0.0268
|
0.426
|
| DEMetro_Z_vs_SMC |
0.5
|
1.919
|
0.0649
|
0.350
|
| DEMetro_Z_vs_SMC |
0.9
|
2.569
|
0.0156
|
0.469
|
| DEMetro_Z_vs_SMC |
0.95
|
2.701
|
0.0114
|
0.493
|
| DEMetro_Z_vs_SMC |
0.99
|
5.197
|
1.47e-05
|
0.949
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
6.800 |
0.108 |
0.073 |
91.927 |
| HMC |
0.3 |
6.631 |
0.096 |
0.065 |
100.809 |
| HMC |
0.5 |
3.973 |
0.100 |
0.074 |
52.283 |
| HMC |
0.9 |
0.681 |
0.049 |
0.027 |
23.475 |
| HMC |
0.95 |
0.533 |
0.047 |
0.030 |
15.943 |
| HMC |
0.99 |
0.091 |
0.028 |
0.017 |
3.754 |
| SMC |
0.0 |
0.112 |
0.108 |
0.073 |
0.044 |
| SMC |
0.3 |
0.110 |
0.096 |
0.065 |
0.220 |
| SMC |
0.5 |
0.091 |
0.100 |
0.074 |
-0.127 |
| SMC |
0.9 |
0.056 |
0.049 |
0.027 |
0.271 |
| SMC |
0.95 |
0.049 |
0.047 |
0.030 |
0.063 |
| SMC |
0.99 |
0.030 |
0.028 |
0.017 |
0.098 |
| Metro |
0.0 |
0.914 |
0.108 |
0.073 |
11.064 |
| Metro |
0.3 |
0.605 |
0.096 |
0.065 |
7.847 |
| Metro |
0.5 |
0.422 |
0.100 |
0.074 |
4.339 |
| Metro |
0.9 |
0.244 |
0.049 |
0.027 |
7.240 |
| Metro |
0.95 |
0.186 |
0.047 |
0.030 |
4.539 |
| Metro |
0.99 |
0.147 |
0.028 |
0.017 |
7.114 |
| DEMetro_Z |
0.0 |
0.487 |
0.108 |
0.073 |
5.195 |
| DEMetro_Z |
0.3 |
0.510 |
0.096 |
0.065 |
6.386 |
| DEMetro_Z |
0.5 |
0.607 |
0.100 |
0.074 |
6.836 |
| DEMetro_Z |
0.9 |
0.292 |
0.049 |
0.027 |
9.034 |
| DEMetro_Z |
0.95 |
0.148 |
0.047 |
0.030 |
3.310 |
| DEMetro_Z |
0.99 |
0.075 |
0.028 |
0.017 |
2.788 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
11.258 |
4.09e-12 |
64.666 |
| HMC |
0.3 |
12.261 |
5.16e-13 |
62.402 |
| HMC |
0.5 |
7.774 |
1.41e-08 |
45.987 |
| HMC |
0.9 |
7.790 |
1.32e-08 |
28.731 |
| HMC |
0.95 |
10.456 |
2.28e-11 |
45.343 |
| HMC |
0.99 |
8.428 |
2.43e-09 |
17.599 |
| SMC |
0.0 |
0.567 |
0.573 |
0.151 |
| SMC |
0.3 |
-0.275 |
0.784 |
-0.064 |
| SMC |
0.5 |
-1.356 |
0.181 |
-0.300 |
| SMC |
0.9 |
0.438 |
0.663 |
0.101 |
| SMC |
0.95 |
-0.650 |
0.518 |
-0.154 |
| SMC |
0.99 |
1.160 |
0.251 |
0.307 |
| Metro |
0.0 |
5.591 |
4.82e-06 |
18.596 |
| Metro |
0.3 |
6.409 |
4.85e-07 |
13.229 |
| Metro |
0.5 |
5.567 |
4.99e-06 |
11.444 |
| Metro |
0.9 |
7.494 |
2.24e-08 |
9.463 |
| Metro |
0.95 |
11.137 |
2.24e-12 |
10.941 |
| Metro |
0.99 |
5.768 |
2.89e-06 |
13.867 |
| DEMetro_Z |
0.0 |
4.695 |
5.77e-05 |
11.463 |
| DEMetro_Z |
0.3 |
3.419 |
0.00186 |
7.688 |
| DEMetro_Z |
0.5 |
3.407 |
0.00193 |
10.084 |
| DEMetro_Z |
0.9 |
3.718 |
0.000846 |
10.080 |
| DEMetro_Z |
0.95 |
4.205 |
0.000225 |
10.674 |
| DEMetro_Z |
0.99 |
6.111 |
9.17e-07 |
6.382 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
1.991
|
0.056
|
0.363
|
| Metro_vs_DEMetro_Z |
0.3
|
1.730
|
0.0943
|
0.316
|
| Metro_vs_DEMetro_Z |
0.5
|
0.367
|
0.716
|
0.067
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.191
|
0.85
|
-0.035
|
| Metro_vs_DEMetro_Z |
0.95
|
0.096
|
0.924
|
0.018
|
| Metro_vs_DEMetro_Z |
0.99
|
2.751
|
0.0101
|
0.502
|
| DEMetro_Z_vs_SMC |
0.0
|
4.545
|
8.97e-05
|
0.830
|
| DEMetro_Z_vs_SMC |
0.3
|
3.519
|
0.00145
|
0.642
|
| DEMetro_Z_vs_SMC |
0.5
|
3.512
|
0.00148
|
0.641
|
| DEMetro_Z_vs_SMC |
0.9
|
3.733
|
0.000823
|
0.681
|
| DEMetro_Z_vs_SMC |
0.95
|
4.221
|
0.000219
|
0.771
|
| DEMetro_Z_vs_SMC |
0.99
|
5.769
|
3e-06
|
1.053
|
| HMC_vs_DEMetro_Z |
0.0
|
8.225
|
4.54e-09
|
1.502
|
| HMC_vs_DEMetro_Z |
0.3
|
10.141
|
4.79e-11
|
1.852
|
| HMC_vs_DEMetro_Z |
0.5
|
5.189
|
1.5e-05
|
0.947
|
| HMC_vs_DEMetro_Z |
0.9
|
4.128
|
0.000283
|
0.754
|
| HMC_vs_DEMetro_Z |
0.95
|
6.462
|
4.52e-07
|
1.180
|
| HMC_vs_DEMetro_Z |
0.99
|
5.093
|
1.96e-05
|
0.930
|
| HMC_vs_Metro |
0.0
|
7.148
|
7.24e-08
|
1.305
|
| HMC_vs_Metro |
0.3
|
8.323
|
3.56e-09
|
1.520
|
| HMC_vs_Metro |
0.5
|
5.265
|
1.22e-05
|
0.961
|
| HMC_vs_Metro |
0.9
|
4.586
|
8.01e-05
|
0.837
|
| HMC_vs_Metro |
0.95
|
7.350
|
4.26e-08
|
1.342
|
| HMC_vs_Metro |
0.99
|
1.371
|
0.181
|
0.250
|
| HMC_vs_SMC |
0.0
|
11.210
|
4.65e-12
|
2.047
|
| HMC_vs_SMC |
0.3
|
12.266
|
5.31e-13
|
2.239
|
| HMC_vs_SMC |
0.5
|
7.866
|
1.13e-08
|
1.436
|
| HMC_vs_SMC |
0.9
|
7.780
|
1.4e-08
|
1.421
|
| HMC_vs_SMC |
0.95
|
10.524
|
2.04e-11
|
1.921
|
| HMC_vs_SMC |
0.99
|
8.274
|
4.03e-09
|
1.511
|
| Metro_vs_SMC |
0.0
|
5.485
|
6.59e-06
|
1.001
|
| Metro_vs_SMC |
0.3
|
6.485
|
4.25e-07
|
1.184
|
| Metro_vs_SMC |
0.5
|
5.706
|
3.58e-06
|
1.042
|
| Metro_vs_SMC |
0.9
|
7.277
|
5.15e-08
|
1.329
|
| Metro_vs_SMC |
0.95
|
11.561
|
2.23e-12
|
2.111
|
| Metro_vs_SMC |
0.99
|
5.815
|
2.65e-06
|
1.062
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.733 |
0.063 |
0.026 |
64.666 |
| HMC |
0.3 |
1.813 |
0.064 |
0.028 |
62.402 |
| HMC |
0.5 |
1.248 |
0.061 |
0.026 |
45.987 |
| HMC |
0.9 |
0.538 |
0.041 |
0.017 |
28.731 |
| HMC |
0.95 |
0.509 |
0.034 |
0.010 |
45.343 |
| HMC |
0.99 |
0.160 |
0.027 |
0.008 |
17.599 |
| SMC |
0.0 |
0.067 |
0.063 |
0.026 |
0.151 |
| SMC |
0.3 |
0.062 |
0.064 |
0.028 |
-0.064 |
| SMC |
0.5 |
0.054 |
0.061 |
0.026 |
-0.300 |
| SMC |
0.9 |
0.042 |
0.041 |
0.017 |
0.101 |
| SMC |
0.95 |
0.032 |
0.034 |
0.010 |
-0.154 |
| SMC |
0.99 |
0.029 |
0.027 |
0.008 |
0.307 |
| Metro |
0.0 |
0.543 |
0.063 |
0.026 |
18.596 |
| Metro |
0.3 |
0.435 |
0.064 |
0.028 |
13.229 |
| Metro |
0.5 |
0.357 |
0.061 |
0.026 |
11.444 |
| Metro |
0.9 |
0.204 |
0.041 |
0.017 |
9.463 |
| Metro |
0.95 |
0.148 |
0.034 |
0.010 |
10.941 |
| Metro |
0.99 |
0.131 |
0.027 |
0.008 |
13.867 |
| DEMetro_Z |
0.0 |
0.359 |
0.063 |
0.026 |
11.463 |
| DEMetro_Z |
0.3 |
0.279 |
0.064 |
0.028 |
7.688 |
| DEMetro_Z |
0.5 |
0.321 |
0.061 |
0.026 |
10.084 |
| DEMetro_Z |
0.9 |
0.215 |
0.041 |
0.017 |
10.080 |
| DEMetro_Z |
0.95 |
0.146 |
0.034 |
0.010 |
10.674 |
| DEMetro_Z |
0.99 |
0.075 |
0.027 |
0.008 |
6.382 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
11.419 |
2.92e-12 |
65.989 |
| HMC |
0.3 |
12.890 |
1.49e-13 |
58.765 |
| HMC |
0.5 |
7.596 |
2.22e-08 |
41.761 |
| HMC |
0.9 |
7.719 |
1.59e-08 |
28.964 |
| HMC |
0.95 |
10.140 |
4.59e-11 |
40.067 |
| HMC |
0.99 |
9.221 |
3.44e-10 |
18.440 |
| SMC |
0.0 |
0.124 |
0.902 |
0.032 |
| SMC |
0.3 |
-0.544 |
0.589 |
-0.125 |
| SMC |
0.5 |
-1.522 |
0.134 |
-0.333 |
| SMC |
0.9 |
0.674 |
0.503 |
0.150 |
| SMC |
0.95 |
-0.375 |
0.709 |
-0.088 |
| SMC |
0.99 |
1.529 |
0.132 |
0.413 |
| Metro |
0.0 |
5.643 |
4.16e-06 |
18.023 |
| Metro |
0.3 |
6.399 |
4.94e-07 |
12.330 |
| Metro |
0.5 |
5.479 |
6.23e-06 |
9.337 |
| Metro |
0.9 |
7.853 |
8.02e-09 |
8.791 |
| Metro |
0.95 |
10.672 |
4.42e-12 |
8.698 |
| Metro |
0.99 |
7.229 |
4.95e-08 |
11.082 |
| DEMetro_Z |
0.0 |
4.647 |
6.58e-05 |
10.863 |
| DEMetro_Z |
0.3 |
3.287 |
0.00262 |
6.946 |
| DEMetro_Z |
0.5 |
3.130 |
0.00394 |
8.211 |
| DEMetro_Z |
0.9 |
3.492 |
0.00154 |
9.838 |
| DEMetro_Z |
0.95 |
3.862 |
0.000573 |
9.192 |
| DEMetro_Z |
0.99 |
5.325 |
8.67e-06 |
5.698 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
4.561
|
8.58e-05
|
0.833
|
| DEMetro_Z_vs_SMC |
0.3
|
3.401
|
0.00198
|
0.621
|
| DEMetro_Z_vs_SMC |
0.5
|
3.260
|
0.00284
|
0.595
|
| DEMetro_Z_vs_SMC |
0.9
|
3.486
|
0.00158
|
0.636
|
| DEMetro_Z_vs_SMC |
0.95
|
3.857
|
0.000588
|
0.704
|
| DEMetro_Z_vs_SMC |
0.99
|
4.883
|
3.51e-05
|
0.892
|
| HMC_vs_Metro |
0.0
|
7.421
|
3.54e-08
|
1.355
|
| HMC_vs_Metro |
0.3
|
8.872
|
9.27e-10
|
1.620
|
| HMC_vs_Metro |
0.5
|
5.436
|
7.56e-06
|
0.992
|
| HMC_vs_Metro |
0.9
|
4.821
|
4.17e-05
|
0.880
|
| HMC_vs_Metro |
0.95
|
7.456
|
3.24e-08
|
1.361
|
| HMC_vs_Metro |
0.99
|
3.335
|
0.00235
|
0.609
|
| Metro_vs_DEMetro_Z |
0.0
|
2.036
|
0.051
|
0.372
|
| Metro_vs_DEMetro_Z |
0.3
|
1.802
|
0.0819
|
0.329
|
| Metro_vs_DEMetro_Z |
0.5
|
0.353
|
0.727
|
0.064
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.324
|
0.748
|
-0.059
|
| Metro_vs_DEMetro_Z |
0.95
|
-0.192
|
0.849
|
-0.035
|
| Metro_vs_DEMetro_Z |
0.99
|
2.660
|
0.0126
|
0.486
|
| HMC_vs_SMC |
0.0
|
11.394
|
3.16e-12
|
2.080
|
| HMC_vs_SMC |
0.3
|
12.964
|
1.35e-13
|
2.367
|
| HMC_vs_SMC |
0.5
|
7.699
|
1.73e-08
|
1.406
|
| HMC_vs_SMC |
0.9
|
7.715
|
1.66e-08
|
1.409
|
| HMC_vs_SMC |
0.95
|
10.201
|
4.19e-11
|
1.862
|
| HMC_vs_SMC |
0.99
|
9.048
|
6.07e-10
|
1.652
|
| Metro_vs_SMC |
0.0
|
5.584
|
5.02e-06
|
1.019
|
| Metro_vs_SMC |
0.3
|
6.556
|
3.51e-07
|
1.197
|
| Metro_vs_SMC |
0.5
|
5.635
|
4.35e-06
|
1.029
|
| Metro_vs_SMC |
0.9
|
7.676
|
1.83e-08
|
1.401
|
| Metro_vs_SMC |
0.95
|
11.457
|
2.77e-12
|
2.092
|
| Metro_vs_SMC |
0.99
|
7.139
|
7.4e-08
|
1.303
|
| HMC_vs_DEMetro_Z |
0.0
|
8.550
|
2.03e-09
|
1.561
|
| HMC_vs_DEMetro_Z |
0.3
|
10.915
|
8.72e-12
|
1.993
|
| HMC_vs_DEMetro_Z |
0.5
|
5.245
|
1.28e-05
|
0.958
|
| HMC_vs_DEMetro_Z |
0.9
|
4.106
|
0.0003
|
0.750
|
| HMC_vs_DEMetro_Z |
0.95
|
6.174
|
9.88e-07
|
1.127
|
| HMC_vs_DEMetro_Z |
0.99
|
6.232
|
8.43e-07
|
1.138
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.430 |
0.013 |
0.006 |
65.989 |
| HMC |
0.3 |
0.451 |
0.013 |
0.007 |
58.765 |
| HMC |
0.5 |
0.346 |
0.013 |
0.008 |
41.761 |
| HMC |
0.9 |
0.220 |
0.013 |
0.007 |
28.964 |
| HMC |
0.95 |
0.246 |
0.013 |
0.006 |
40.067 |
| HMC |
0.99 |
0.103 |
0.013 |
0.005 |
18.440 |
| SMC |
0.0 |
0.013 |
0.013 |
0.006 |
0.032 |
| SMC |
0.3 |
0.012 |
0.013 |
0.007 |
-0.125 |
| SMC |
0.5 |
0.011 |
0.013 |
0.008 |
-0.333 |
| SMC |
0.9 |
0.014 |
0.013 |
0.007 |
0.150 |
| SMC |
0.95 |
0.013 |
0.013 |
0.006 |
-0.088 |
| SMC |
0.99 |
0.015 |
0.013 |
0.005 |
0.413 |
| Metro |
0.0 |
0.127 |
0.013 |
0.006 |
18.023 |
| Metro |
0.3 |
0.105 |
0.013 |
0.007 |
12.330 |
| Metro |
0.5 |
0.088 |
0.013 |
0.008 |
9.337 |
| Metro |
0.9 |
0.076 |
0.013 |
0.007 |
8.791 |
| Metro |
0.95 |
0.064 |
0.013 |
0.006 |
8.698 |
| Metro |
0.99 |
0.067 |
0.013 |
0.005 |
11.082 |
| DEMetro_Z |
0.0 |
0.081 |
0.013 |
0.006 |
10.863 |
| DEMetro_Z |
0.3 |
0.065 |
0.013 |
0.007 |
6.946 |
| DEMetro_Z |
0.5 |
0.079 |
0.013 |
0.008 |
8.211 |
| DEMetro_Z |
0.9 |
0.083 |
0.013 |
0.007 |
9.838 |
| DEMetro_Z |
0.95 |
0.066 |
0.013 |
0.006 |
9.192 |
| DEMetro_Z |
0.99 |
0.041 |
0.013 |
0.005 |
5.698 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
0.5
0.9
0.95
0.99
Vary_Dimension_with_high_correlation
(MvNormal,
dimension,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.530 |
0.000926 |
1.233 |
| HMC |
3 |
3.489 |
0.000986 |
1.083 |
| HMC |
5 |
3.683 |
0.000733 |
1.915 |
| HMC |
8 |
2.973 |
0.00506 |
1.414 |
| HMC |
15 |
5.263 |
7.7e-06 |
3.335 |
| HMC |
30 |
5.150 |
1.48e-05 |
6.259 |
| SMC |
2 |
-0.380 |
0.706 |
-0.109 |
| SMC |
3 |
-1.091 |
0.281 |
-0.231 |
| SMC |
5 |
0.210 |
0.834 |
0.058 |
| SMC |
8 |
-0.236 |
0.814 |
-0.056 |
| SMC |
15 |
-0.825 |
0.413 |
-0.211 |
| SMC |
30 |
-2.551 |
0.0135 |
-0.736 |
| Metro |
2 |
4.755 |
4.65e-05 |
6.649 |
| Metro |
3 |
6.731 |
1.79e-07 |
8.715 |
| Metro |
5 |
7.392 |
3.58e-08 |
18.868 |
| Metro |
8 |
7.939 |
8.63e-09 |
19.442 |
| Metro |
15 |
6.965 |
1.15e-07 |
28.729 |
| Metro |
30 |
8.038 |
7.15e-09 |
42.409 |
| DEMetro_Z |
2 |
3.226 |
0.0026 |
1.625 |
| DEMetro_Z |
3 |
5.663 |
4.01e-06 |
43.233 |
| DEMetro_Z |
5 |
7.124 |
7.71e-08 |
620.224 |
| DEMetro_Z |
8 |
14.288 |
1.17e-14 |
351.974 |
| DEMetro_Z |
15 |
22.828 |
4.4e-20 |
458.820 |
| DEMetro_Z |
30 |
44.028 |
4.03e-28 |
584.440 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.661
|
0.514
|
-0.121
|
| HMC_vs_DEMetro_Z |
1
|
-5.542
|
5.63e-06
|
-1.012
|
| HMC_vs_DEMetro_Z |
2
|
-7.108
|
8.03e-08
|
-1.298
|
| HMC_vs_DEMetro_Z |
3
|
-14.302
|
1.14e-14
|
-2.611
|
| HMC_vs_DEMetro_Z |
4
|
-22.559
|
6.14e-20
|
-4.119
|
| HMC_vs_DEMetro_Z |
5
|
-43.280
|
6.69e-28
|
-7.902
|
| Metro_vs_SMC |
0
|
4.711
|
5.66e-05
|
0.860
|
| Metro_vs_SMC |
1
|
6.950
|
1.22e-07
|
1.269
|
| Metro_vs_SMC |
2
|
7.350
|
4.27e-08
|
1.342
|
| Metro_vs_SMC |
3
|
7.950
|
9.1e-09
|
1.451
|
| Metro_vs_SMC |
4
|
7.193
|
6.43e-08
|
1.313
|
| Metro_vs_SMC |
5
|
8.071
|
6.7e-09
|
1.473
|
| Metro_vs_DEMetro_Z |
0
|
3.467
|
0.00166
|
0.633
|
| Metro_vs_DEMetro_Z |
1
|
-4.373
|
0.000144
|
-0.798
|
| Metro_vs_DEMetro_Z |
2
|
-6.940
|
1.25e-07
|
-1.267
|
| Metro_vs_DEMetro_Z |
3
|
-13.455
|
5.36e-14
|
-2.456
|
| Metro_vs_DEMetro_Z |
4
|
-21.275
|
3.06e-19
|
-3.884
|
| Metro_vs_DEMetro_Z |
5
|
-40.251
|
5.31e-27
|
-7.349
|
| HMC_vs_Metro |
0
|
-4.019
|
0.00038
|
-0.734
|
| HMC_vs_Metro |
1
|
-5.979
|
1.69e-06
|
-1.092
|
| HMC_vs_Metro |
2
|
-6.985
|
1.11e-07
|
-1.275
|
| HMC_vs_Metro |
3
|
-6.992
|
1.09e-07
|
-1.277
|
| HMC_vs_Metro |
4
|
-5.877
|
2.23e-06
|
-1.073
|
| HMC_vs_Metro |
5
|
-6.327
|
6.52e-07
|
-1.155
|
| HMC_vs_SMC |
0
|
3.274
|
0.00275
|
0.598
|
| HMC_vs_SMC |
1
|
4.092
|
0.000312
|
0.747
|
| HMC_vs_SMC |
2
|
4.434
|
0.000122
|
0.810
|
| HMC_vs_SMC |
3
|
3.011
|
0.00536
|
0.550
|
| HMC_vs_SMC |
4
|
5.263
|
1.22e-05
|
0.961
|
| HMC_vs_SMC |
5
|
5.650
|
4.18e-06
|
1.031
|
| DEMetro_Z_vs_SMC |
0
|
3.353
|
0.00224
|
0.612
|
| DEMetro_Z_vs_SMC |
1
|
5.694
|
3.7e-06
|
1.040
|
| DEMetro_Z_vs_SMC |
2
|
7.125
|
7.68e-08
|
1.301
|
| DEMetro_Z_vs_SMC |
3
|
14.285
|
1.18e-14
|
2.608
|
| DEMetro_Z_vs_SMC |
4
|
22.839
|
4.37e-20
|
4.170
|
| DEMetro_Z_vs_SMC |
5
|
43.987
|
4.21e-28
|
8.031
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.037 |
0.022 |
0.012 |
1.233 |
| HMC |
3 |
0.036 |
0.019 |
0.016 |
1.083 |
| HMC |
5 |
0.036 |
0.017 |
0.010 |
1.915 |
| HMC |
8 |
0.039 |
0.019 |
0.014 |
1.414 |
| HMC |
15 |
0.060 |
0.019 |
0.012 |
3.335 |
| HMC |
30 |
0.093 |
0.024 |
0.011 |
6.259 |
| SMC |
2 |
0.020 |
0.022 |
0.012 |
-0.109 |
| SMC |
3 |
0.015 |
0.019 |
0.016 |
-0.231 |
| SMC |
5 |
0.017 |
0.017 |
0.010 |
0.058 |
| SMC |
8 |
0.018 |
0.019 |
0.014 |
-0.056 |
| SMC |
15 |
0.016 |
0.019 |
0.012 |
-0.211 |
| SMC |
30 |
0.016 |
0.024 |
0.011 |
-0.736 |
| Metro |
2 |
0.102 |
0.022 |
0.012 |
6.649 |
| Metro |
3 |
0.154 |
0.019 |
0.016 |
8.715 |
| Metro |
5 |
0.207 |
0.017 |
0.010 |
18.868 |
| Metro |
8 |
0.298 |
0.019 |
0.014 |
19.442 |
| Metro |
15 |
0.376 |
0.019 |
0.012 |
28.729 |
| Metro |
30 |
0.491 |
0.024 |
0.011 |
42.409 |
| DEMetro_Z |
2 |
0.041 |
0.022 |
0.012 |
1.625 |
| DEMetro_Z |
3 |
0.690 |
0.019 |
0.016 |
43.233 |
| DEMetro_Z |
5 |
6.255 |
0.017 |
0.010 |
620.224 |
| DEMetro_Z |
8 |
5.087 |
0.019 |
0.014 |
351.974 |
| DEMetro_Z |
15 |
5.722 |
0.019 |
0.012 |
458.820 |
| DEMetro_Z |
30 |
6.461 |
0.024 |
0.011 |
584.440 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
4.501 |
6.53e-05 |
2.349 |
| HMC |
3 |
2.978 |
0.00484 |
1.273 |
| HMC |
5 |
4.326 |
0.000115 |
2.395 |
| HMC |
8 |
3.909 |
0.000361 |
1.855 |
| HMC |
15 |
7.083 |
4.53e-08 |
5.418 |
| HMC |
30 |
5.044 |
1.73e-05 |
4.069 |
| SMC |
2 |
2.573 |
0.0135 |
0.983 |
| SMC |
3 |
-1.010 |
0.317 |
-0.256 |
| SMC |
5 |
-1.060 |
0.293 |
-0.269 |
| SMC |
8 |
0.312 |
0.756 |
0.072 |
| SMC |
15 |
1.344 |
0.185 |
0.443 |
| SMC |
30 |
-0.392 |
0.697 |
-0.091 |
| Metro |
2 |
6.559 |
2.9e-07 |
8.700 |
| Metro |
3 |
7.771 |
1.1e-08 |
10.117 |
| Metro |
5 |
9.192 |
3.41e-10 |
15.064 |
| Metro |
8 |
6.798 |
1.63e-07 |
11.794 |
| Metro |
15 |
6.469 |
4.37e-07 |
29.758 |
| Metro |
30 |
5.784 |
2.86e-06 |
26.944 |
| DEMetro_Z |
2 |
5.204 |
9.36e-06 |
3.370 |
| DEMetro_Z |
3 |
4.855 |
3.8e-05 |
965.993 |
| DEMetro_Z |
5 |
7.736 |
1.57e-08 |
7935.116 |
| DEMetro_Z |
8 |
12.065 |
7.95e-13 |
6074.478 |
| DEMetro_Z |
15 |
21.018 |
4.25e-19 |
10205.749 |
| DEMetro_Z |
30 |
41.377 |
2.42e-27 |
7838.341 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.443
|
0.0209
|
0.446
|
| HMC_vs_SMC |
1
|
3.268
|
0.00278
|
0.597
|
| HMC_vs_SMC |
2
|
5.006
|
2.5e-05
|
0.914
|
| HMC_vs_SMC |
3
|
3.862
|
0.000581
|
0.705
|
| HMC_vs_SMC |
4
|
6.466
|
4.48e-07
|
1.180
|
| HMC_vs_SMC |
5
|
5.216
|
1.39e-05
|
0.952
|
| Metro_vs_DEMetro_Z |
0
|
3.711
|
0.000872
|
0.678
|
| Metro_vs_DEMetro_Z |
1
|
-4.796
|
4.48e-05
|
-0.876
|
| Metro_vs_DEMetro_Z |
2
|
-7.721
|
1.63e-08
|
-1.410
|
| Metro_vs_DEMetro_Z |
3
|
-12.037
|
8.4e-13
|
-2.198
|
| Metro_vs_DEMetro_Z |
4
|
-20.953
|
4.63e-19
|
-3.825
|
| Metro_vs_DEMetro_Z |
5
|
-41.305
|
2.54e-27
|
-7.541
|
| HMC_vs_Metro |
0
|
-4.359
|
0.00015
|
-0.796
|
| HMC_vs_Metro |
1
|
-6.590
|
3.2e-07
|
-1.203
|
| HMC_vs_Metro |
2
|
-8.393
|
3e-09
|
-1.532
|
| HMC_vs_Metro |
3
|
-5.536
|
5.73e-06
|
-1.011
|
| HMC_vs_Metro |
4
|
-5.361
|
9.31e-06
|
-0.979
|
| HMC_vs_Metro |
5
|
-5.022
|
2.39e-05
|
-0.917
|
| HMC_vs_DEMetro_Z |
0
|
-1.471
|
0.152
|
-0.269
|
| HMC_vs_DEMetro_Z |
1
|
-4.845
|
3.9e-05
|
-0.885
|
| HMC_vs_DEMetro_Z |
2
|
-7.733
|
1.58e-08
|
-1.412
|
| HMC_vs_DEMetro_Z |
3
|
-12.061
|
8e-13
|
-2.202
|
| HMC_vs_DEMetro_Z |
4
|
-20.997
|
4.38e-19
|
-3.833
|
| HMC_vs_DEMetro_Z |
5
|
-41.328
|
2.5e-27
|
-7.545
|
| Metro_vs_SMC |
0
|
5.303
|
1.09e-05
|
0.968
|
| Metro_vs_SMC |
1
|
8.228
|
4.52e-09
|
1.502
|
| Metro_vs_SMC |
2
|
9.332
|
3.09e-10
|
1.704
|
| Metro_vs_SMC |
3
|
6.801
|
1.82e-07
|
1.242
|
| Metro_vs_SMC |
4
|
6.288
|
7.25e-07
|
1.148
|
| Metro_vs_SMC |
5
|
5.819
|
2.62e-06
|
1.062
|
| DEMetro_Z_vs_SMC |
0
|
3.209
|
0.00324
|
0.586
|
| DEMetro_Z_vs_SMC |
1
|
4.857
|
3.78e-05
|
0.887
|
| DEMetro_Z_vs_SMC |
2
|
7.736
|
1.57e-08
|
1.412
|
| DEMetro_Z_vs_SMC |
3
|
12.064
|
7.95e-13
|
2.203
|
| DEMetro_Z_vs_SMC |
4
|
21.017
|
4.26e-19
|
3.837
|
| DEMetro_Z_vs_SMC |
5
|
41.371
|
2.43e-27
|
7.553
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.045 |
0.019 |
0.011 |
2.349 |
| HMC |
3 |
0.054 |
0.030 |
0.019 |
1.273 |
| HMC |
5 |
0.065 |
0.028 |
0.015 |
2.395 |
| HMC |
8 |
0.059 |
0.026 |
0.018 |
1.855 |
| HMC |
15 |
0.094 |
0.024 |
0.013 |
5.418 |
| HMC |
30 |
0.117 |
0.029 |
0.022 |
4.069 |
| SMC |
2 |
0.030 |
0.019 |
0.011 |
0.983 |
| SMC |
3 |
0.025 |
0.030 |
0.019 |
-0.256 |
| SMC |
5 |
0.024 |
0.028 |
0.015 |
-0.269 |
| SMC |
8 |
0.027 |
0.026 |
0.018 |
0.072 |
| SMC |
15 |
0.030 |
0.024 |
0.013 |
0.443 |
| SMC |
30 |
0.027 |
0.029 |
0.022 |
-0.091 |
| Metro |
2 |
0.115 |
0.019 |
0.011 |
8.700 |
| Metro |
3 |
0.223 |
0.030 |
0.019 |
10.117 |
| Metro |
5 |
0.258 |
0.028 |
0.015 |
15.064 |
| Metro |
8 |
0.235 |
0.026 |
0.018 |
11.794 |
| Metro |
15 |
0.405 |
0.024 |
0.013 |
29.758 |
| Metro |
30 |
0.609 |
0.029 |
0.022 |
26.944 |
| DEMetro_Z |
2 |
0.056 |
0.019 |
0.011 |
3.370 |
| DEMetro_Z |
3 |
18.389 |
0.030 |
0.019 |
965.993 |
| DEMetro_Z |
5 |
120.893 |
0.028 |
0.015 |
7935.116 |
| DEMetro_Z |
8 |
107.824 |
0.026 |
0.018 |
6074.478 |
| DEMetro_Z |
15 |
130.735 |
0.024 |
0.013 |
10205.749 |
| DEMetro_Z |
30 |
168.762 |
0.029 |
0.022 |
7838.341 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
4.793 |
1.63e-05 |
1.678 |
| HMC |
3 |
4.638 |
2.54e-05 |
1.539 |
| HMC |
5 |
5.868 |
1.43e-06 |
4.243 |
| HMC |
8 |
4.768 |
2.86e-05 |
2.463 |
| HMC |
15 |
7.717 |
8.25e-09 |
6.211 |
| HMC |
30 |
7.656 |
1.53e-08 |
10.688 |
| SMC |
2 |
0.243 |
0.809 |
0.071 |
| SMC |
3 |
-1.697 |
0.0973 |
-0.340 |
| SMC |
5 |
0.519 |
0.606 |
0.167 |
| SMC |
8 |
-0.497 |
0.621 |
-0.128 |
| SMC |
15 |
0.345 |
0.731 |
0.100 |
| SMC |
30 |
-2.364 |
0.0215 |
-0.653 |
| Metro |
2 |
6.902 |
1.2e-07 |
10.863 |
| Metro |
3 |
10.446 |
1.45e-11 |
12.798 |
| Metro |
5 |
11.020 |
6.54e-12 |
40.437 |
| Metro |
8 |
9.681 |
1.27e-10 |
29.219 |
| Metro |
15 |
8.493 |
2.3e-09 |
50.176 |
| Metro |
30 |
11.465 |
2.66e-12 |
69.260 |
| DEMetro_Z |
2 |
6.482 |
1.39e-07 |
3.359 |
| DEMetro_Z |
3 |
8.585 |
1.85e-09 |
83.304 |
| DEMetro_Z |
5 |
12.943 |
1.41e-13 |
1833.818 |
| DEMetro_Z |
8 |
28.280 |
1.15e-22 |
956.499 |
| DEMetro_Z |
15 |
49.920 |
1.12e-29 |
1343.122 |
| DEMetro_Z |
30 |
74.499 |
1.11e-34 |
1562.633 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
4.765
|
4.88e-05
|
0.870
|
| Metro_vs_DEMetro_Z |
1
|
-7.048
|
9.42e-08
|
-1.287
|
| Metro_vs_DEMetro_Z |
2
|
-12.675
|
2.37e-13
|
-2.314
|
| Metro_vs_DEMetro_Z |
3
|
-27.604
|
2.27e-22
|
-5.040
|
| Metro_vs_DEMetro_Z |
4
|
-47.389
|
5e-29
|
-8.652
|
| Metro_vs_DEMetro_Z |
5
|
-70.084
|
6.5e-34
|
-12.795
|
| DEMetro_Z_vs_SMC |
0
|
5.699
|
3.65e-06
|
1.040
|
| DEMetro_Z_vs_SMC |
1
|
8.649
|
1.59e-09
|
1.579
|
| DEMetro_Z_vs_SMC |
2
|
12.940
|
1.42e-13
|
2.363
|
| DEMetro_Z_vs_SMC |
3
|
28.319
|
1.11e-22
|
5.170
|
| DEMetro_Z_vs_SMC |
4
|
49.969
|
1.09e-29
|
9.123
|
| DEMetro_Z_vs_SMC |
5
|
74.453
|
1.14e-34
|
13.593
|
| HMC_vs_DEMetro_Z |
0
|
-2.920
|
0.00671
|
-0.533
|
| HMC_vs_DEMetro_Z |
1
|
-8.396
|
2.97e-09
|
-1.533
|
| HMC_vs_DEMetro_Z |
2
|
-12.917
|
1.48e-13
|
-2.358
|
| HMC_vs_DEMetro_Z |
3
|
-28.146
|
1.32e-22
|
-5.139
|
| HMC_vs_DEMetro_Z |
4
|
-49.170
|
1.74e-29
|
-8.977
|
| HMC_vs_DEMetro_Z |
5
|
-73.883
|
1.42e-34
|
-13.489
|
| HMC_vs_Metro |
0
|
-6.133
|
1.11e-06
|
-1.120
|
| HMC_vs_Metro |
1
|
-9.165
|
4.59e-10
|
-1.673
|
| HMC_vs_Metro |
2
|
-10.211
|
4.1e-11
|
-1.864
|
| HMC_vs_Metro |
3
|
-8.575
|
1.91e-09
|
-1.566
|
| HMC_vs_Metro |
4
|
-7.265
|
5.33e-08
|
-1.326
|
| HMC_vs_Metro |
5
|
-9.032
|
6.31e-10
|
-1.649
|
| HMC_vs_SMC |
0
|
3.868
|
0.000571
|
0.706
|
| HMC_vs_SMC |
1
|
6.028
|
1.48e-06
|
1.101
|
| HMC_vs_SMC |
2
|
6.214
|
8.88e-07
|
1.134
|
| HMC_vs_SMC |
3
|
4.749
|
5.09e-05
|
0.867
|
| HMC_vs_SMC |
4
|
7.022
|
1.01e-07
|
1.282
|
| HMC_vs_SMC |
5
|
7.913
|
1e-08
|
1.445
|
| Metro_vs_SMC |
0
|
6.676
|
2.54e-07
|
1.219
|
| Metro_vs_SMC |
1
|
10.767
|
1.2e-11
|
1.966
|
| Metro_vs_SMC |
2
|
10.859
|
9.85e-12
|
1.983
|
| Metro_vs_SMC |
3
|
9.659
|
1.44e-10
|
1.763
|
| Metro_vs_SMC |
4
|
8.655
|
1.57e-09
|
1.580
|
| Metro_vs_SMC |
5
|
11.536
|
2.35e-12
|
2.106
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.041 |
0.027 |
0.008 |
1.678 |
| HMC |
3 |
0.044 |
0.028 |
0.011 |
1.539 |
| HMC |
5 |
0.043 |
0.023 |
0.005 |
4.243 |
| HMC |
8 |
0.046 |
0.025 |
0.008 |
2.463 |
| HMC |
15 |
0.065 |
0.024 |
0.007 |
6.211 |
| HMC |
30 |
0.098 |
0.028 |
0.007 |
10.688 |
| SMC |
2 |
0.028 |
0.027 |
0.008 |
0.071 |
| SMC |
3 |
0.024 |
0.028 |
0.011 |
-0.340 |
| SMC |
5 |
0.024 |
0.023 |
0.005 |
0.167 |
| SMC |
8 |
0.024 |
0.025 |
0.008 |
-0.128 |
| SMC |
15 |
0.024 |
0.024 |
0.007 |
0.100 |
| SMC |
30 |
0.023 |
0.028 |
0.007 |
-0.653 |
| Metro |
2 |
0.115 |
0.027 |
0.008 |
10.863 |
| Metro |
3 |
0.166 |
0.028 |
0.011 |
12.798 |
| Metro |
5 |
0.212 |
0.023 |
0.005 |
40.437 |
| Metro |
8 |
0.268 |
0.025 |
0.008 |
29.219 |
| Metro |
15 |
0.362 |
0.024 |
0.007 |
50.176 |
| Metro |
30 |
0.484 |
0.028 |
0.007 |
69.260 |
| DEMetro_Z |
2 |
0.054 |
0.027 |
0.008 |
3.359 |
| DEMetro_Z |
3 |
0.932 |
0.028 |
0.011 |
83.304 |
| DEMetro_Z |
5 |
8.574 |
0.023 |
0.005 |
1833.818 |
| DEMetro_Z |
8 |
7.987 |
0.025 |
0.008 |
956.499 |
| DEMetro_Z |
15 |
9.072 |
0.024 |
0.007 |
1343.122 |
| DEMetro_Z |
30 |
10.322 |
0.028 |
0.007 |
1562.633 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.937 |
0.000245 |
1.240 |
| HMC |
3 |
4.750 |
1.59e-05 |
1.473 |
| HMC |
5 |
5.299 |
7.55e-06 |
3.745 |
| HMC |
8 |
4.806 |
1.96e-05 |
1.980 |
| HMC |
15 |
8.207 |
1.42e-09 |
5.305 |
| HMC |
30 |
8.634 |
1.03e-09 |
9.340 |
| SMC |
2 |
-0.086 |
0.932 |
-0.024 |
| SMC |
3 |
-0.894 |
0.376 |
-0.193 |
| SMC |
5 |
0.445 |
0.658 |
0.145 |
| SMC |
8 |
-0.020 |
0.984 |
-0.005 |
| SMC |
15 |
0.375 |
0.709 |
0.103 |
| SMC |
30 |
-1.835 |
0.0716 |
-0.454 |
| Metro |
2 |
7.353 |
3.44e-08 |
10.333 |
| Metro |
3 |
11.022 |
3.08e-12 |
11.224 |
| Metro |
5 |
12.420 |
3.46e-13 |
35.650 |
| Metro |
8 |
10.783 |
9.72e-12 |
23.043 |
| Metro |
15 |
11.119 |
5.32e-12 |
41.830 |
| Metro |
30 |
14.180 |
1.31e-14 |
56.008 |
| DEMetro_Z |
2 |
6.353 |
1.83e-07 |
3.099 |
| DEMetro_Z |
3 |
12.823 |
6.91e-14 |
13.512 |
| DEMetro_Z |
5 |
33.890 |
6.55e-25 |
206.092 |
| DEMetro_Z |
8 |
56.453 |
1.02e-31 |
99.767 |
| DEMetro_Z |
15 |
59.059 |
3.7e-32 |
121.021 |
| DEMetro_Z |
30 |
97.598 |
1.05e-39 |
109.776 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.759
|
3.09e-06
|
1.051
|
| DEMetro_Z_vs_SMC |
1
|
13.044
|
1.16e-13
|
2.381
|
| DEMetro_Z_vs_SMC |
2
|
34.174
|
5.56e-25
|
6.239
|
| DEMetro_Z_vs_SMC |
3
|
55.759
|
4.7e-31
|
10.180
|
| DEMetro_Z_vs_SMC |
4
|
57.609
|
1.84e-31
|
10.518
|
| DEMetro_Z_vs_SMC |
5
|
94.237
|
1.26e-37
|
17.205
|
| HMC_vs_Metro |
0
|
-6.768
|
1.99e-07
|
-1.236
|
| HMC_vs_Metro |
1
|
-9.574
|
1.75e-10
|
-1.748
|
| HMC_vs_Metro |
2
|
-11.938
|
1.03e-12
|
-2.180
|
| HMC_vs_Metro |
3
|
-9.630
|
1.54e-10
|
-1.758
|
| HMC_vs_Metro |
4
|
-9.560
|
1.81e-10
|
-1.745
|
| HMC_vs_Metro |
5
|
-10.825
|
1.06e-11
|
-1.976
|
| Metro_vs_DEMetro_Z |
0
|
5.350
|
9.6e-06
|
0.977
|
| Metro_vs_DEMetro_Z |
1
|
-1.523
|
0.139
|
-0.278
|
| Metro_vs_DEMetro_Z |
2
|
-30.116
|
1.97e-23
|
-5.498
|
| Metro_vs_DEMetro_Z |
3
|
-27.832
|
1.8e-22
|
-5.081
|
| Metro_vs_DEMetro_Z |
4
|
-19.441
|
3.53e-18
|
-3.549
|
| Metro_vs_DEMetro_Z |
5
|
-12.821
|
1.79e-13
|
-2.341
|
| HMC_vs_SMC |
0
|
3.616
|
0.00112
|
0.660
|
| HMC_vs_SMC |
1
|
5.895
|
2.13e-06
|
1.076
|
| HMC_vs_SMC |
2
|
5.573
|
5.16e-06
|
1.018
|
| HMC_vs_SMC |
3
|
4.864
|
3.7e-05
|
0.888
|
| HMC_vs_SMC |
4
|
7.605
|
2.2e-08
|
1.389
|
| HMC_vs_SMC |
5
|
8.848
|
9.82e-10
|
1.615
|
| Metro_vs_SMC |
0
|
7.233
|
5.79e-08
|
1.321
|
| Metro_vs_SMC |
1
|
11.485
|
2.61e-12
|
2.097
|
| Metro_vs_SMC |
2
|
12.377
|
4.25e-13
|
2.260
|
| Metro_vs_SMC |
3
|
10.754
|
1.24e-11
|
1.963
|
| Metro_vs_SMC |
4
|
11.297
|
3.87e-12
|
2.062
|
| Metro_vs_SMC |
5
|
14.273
|
1.2e-14
|
2.606
|
| HMC_vs_DEMetro_Z |
0
|
-4.328
|
0.000163
|
-0.790
|
| HMC_vs_DEMetro_Z |
1
|
-11.326
|
3.64e-12
|
-2.068
|
| HMC_vs_DEMetro_Z |
2
|
-33.651
|
8.6e-25
|
-6.144
|
| HMC_vs_DEMetro_Z |
3
|
-57.570
|
1.87e-31
|
-10.511
|
| HMC_vs_DEMetro_Z |
4
|
-60.788
|
3.92e-32
|
-11.098
|
| HMC_vs_DEMetro_Z |
5
|
-65.217
|
5.18e-33
|
-11.907
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.020 |
0.014 |
0.005 |
1.240 |
| HMC |
3 |
0.026 |
0.015 |
0.007 |
1.473 |
| HMC |
5 |
0.026 |
0.013 |
0.003 |
3.745 |
| HMC |
8 |
0.027 |
0.014 |
0.006 |
1.980 |
| HMC |
15 |
0.039 |
0.014 |
0.005 |
5.305 |
| HMC |
30 |
0.063 |
0.016 |
0.005 |
9.340 |
| SMC |
2 |
0.014 |
0.014 |
0.005 |
-0.024 |
| SMC |
3 |
0.013 |
0.015 |
0.007 |
-0.193 |
| SMC |
5 |
0.013 |
0.013 |
0.003 |
0.145 |
| SMC |
8 |
0.014 |
0.014 |
0.006 |
-0.005 |
| SMC |
15 |
0.014 |
0.014 |
0.005 |
0.103 |
| SMC |
30 |
0.014 |
0.016 |
0.005 |
-0.454 |
| Metro |
2 |
0.065 |
0.014 |
0.005 |
10.333 |
| Metro |
3 |
0.098 |
0.015 |
0.007 |
11.224 |
| Metro |
5 |
0.135 |
0.013 |
0.003 |
35.650 |
| Metro |
8 |
0.163 |
0.014 |
0.006 |
23.043 |
| Metro |
15 |
0.214 |
0.014 |
0.005 |
41.830 |
| Metro |
30 |
0.299 |
0.016 |
0.005 |
56.008 |
| DEMetro_Z |
2 |
0.029 |
0.014 |
0.005 |
3.099 |
| DEMetro_Z |
3 |
0.115 |
0.015 |
0.007 |
13.512 |
| DEMetro_Z |
5 |
0.719 |
0.013 |
0.003 |
206.092 |
| DEMetro_Z |
8 |
0.657 |
0.014 |
0.006 |
99.767 |
| DEMetro_Z |
15 |
0.594 |
0.014 |
0.005 |
121.021 |
| DEMetro_Z |
30 |
0.571 |
0.016 |
0.005 |
109.776 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.338 |
0.188 |
0.521 |
| HMC |
3 |
1.149 |
0.255 |
0.341 |
| HMC |
5 |
5.449 |
3.61e-06 |
2.904 |
| HMC |
8 |
4.339 |
9.53e-05 |
1.975 |
| HMC |
15 |
3.368 |
0.00182 |
1.873 |
| HMC |
30 |
6.277 |
5.77e-07 |
6.666 |
| SMC |
2 |
-1.389 |
0.17 |
-0.351 |
| SMC |
3 |
-0.185 |
0.854 |
-0.045 |
| SMC |
5 |
-0.264 |
0.792 |
-0.072 |
| SMC |
8 |
-0.254 |
0.801 |
-0.059 |
| SMC |
15 |
0.157 |
0.876 |
0.044 |
| SMC |
30 |
-1.035 |
0.305 |
-0.291 |
| Metro |
2 |
6.022 |
1.37e-06 |
10.408 |
| Metro |
3 |
7.355 |
3.43e-08 |
10.378 |
| Metro |
5 |
7.699 |
1.66e-08 |
27.186 |
| Metro |
8 |
6.863 |
1.49e-07 |
23.958 |
| Metro |
15 |
6.816 |
1.72e-07 |
34.438 |
| Metro |
30 |
6.775 |
1.94e-07 |
68.745 |
| DEMetro_Z |
2 |
1.418 |
0.164 |
0.604 |
| DEMetro_Z |
3 |
4.377 |
0.00014 |
11.172 |
| DEMetro_Z |
5 |
6.421 |
5.05e-07 |
648.043 |
| DEMetro_Z |
8 |
7.676 |
1.83e-08 |
540.024 |
| DEMetro_Z |
15 |
28.788 |
6.97e-23 |
743.445 |
| DEMetro_Z |
30 |
36.403 |
9.23e-26 |
1011.243 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.154
|
0.879
|
-0.028
|
| HMC_vs_DEMetro_Z |
1
|
-4.117
|
0.000291
|
-0.752
|
| HMC_vs_DEMetro_Z |
2
|
-6.382
|
5.62e-07
|
-1.165
|
| HMC_vs_DEMetro_Z |
3
|
-7.640
|
2.01e-08
|
-1.395
|
| HMC_vs_DEMetro_Z |
4
|
-28.892
|
6.32e-23
|
-5.275
|
| HMC_vs_DEMetro_Z |
5
|
-36.341
|
9.73e-26
|
-6.635
|
| Metro_vs_SMC |
0
|
6.246
|
8.13e-07
|
1.140
|
| Metro_vs_SMC |
1
|
7.388
|
3.86e-08
|
1.349
|
| Metro_vs_SMC |
2
|
7.767
|
1.45e-08
|
1.418
|
| Metro_vs_SMC |
3
|
6.831
|
1.68e-07
|
1.247
|
| Metro_vs_SMC |
4
|
6.878
|
1.48e-07
|
1.256
|
| Metro_vs_SMC |
5
|
6.823
|
1.71e-07
|
1.246
|
| Metro_vs_DEMetro_Z |
0
|
5.570
|
5.21e-06
|
1.017
|
| Metro_vs_DEMetro_Z |
1
|
-0.263
|
0.795
|
-0.048
|
| Metro_vs_DEMetro_Z |
2
|
-6.179
|
9.75e-07
|
-1.128
|
| Metro_vs_DEMetro_Z |
3
|
-7.237
|
5.72e-08
|
-1.321
|
| Metro_vs_DEMetro_Z |
4
|
-25.596
|
1.87e-21
|
-4.673
|
| Metro_vs_DEMetro_Z |
5
|
-35.147
|
2.51e-25
|
-6.417
|
| HMC_vs_Metro |
0
|
-5.940
|
1.88e-06
|
-1.084
|
| HMC_vs_Metro |
1
|
-7.254
|
5.47e-08
|
-1.324
|
| HMC_vs_Metro |
2
|
-6.767
|
1.99e-07
|
-1.235
|
| HMC_vs_Metro |
3
|
-6.398
|
5.38e-07
|
-1.168
|
| HMC_vs_Metro |
4
|
-6.148
|
1.06e-06
|
-1.123
|
| HMC_vs_Metro |
5
|
-6.241
|
8.23e-07
|
-1.140
|
| HMC_vs_SMC |
0
|
2.536
|
0.0169
|
0.463
|
| HMC_vs_SMC |
1
|
1.400
|
0.172
|
0.256
|
| HMC_vs_SMC |
2
|
5.643
|
4.26e-06
|
1.030
|
| HMC_vs_SMC |
3
|
4.640
|
6.88e-05
|
0.847
|
| HMC_vs_SMC |
4
|
3.085
|
0.00444
|
0.563
|
| HMC_vs_SMC |
5
|
6.723
|
2.24e-07
|
1.227
|
| DEMetro_Z_vs_SMC |
0
|
2.202
|
0.0357
|
0.402
|
| DEMetro_Z_vs_SMC |
1
|
4.354
|
0.000152
|
0.795
|
| DEMetro_Z_vs_SMC |
2
|
6.426
|
4.98e-07
|
1.173
|
| DEMetro_Z_vs_SMC |
3
|
7.680
|
1.81e-08
|
1.402
|
| DEMetro_Z_vs_SMC |
4
|
28.834
|
6.7e-23
|
5.264
|
| DEMetro_Z_vs_SMC |
5
|
36.478
|
8.74e-26
|
6.660
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.028 |
0.022 |
0.012 |
0.521 |
| HMC |
3 |
0.024 |
0.019 |
0.016 |
0.341 |
| HMC |
5 |
0.046 |
0.017 |
0.010 |
2.904 |
| HMC |
8 |
0.047 |
0.019 |
0.014 |
1.975 |
| HMC |
15 |
0.042 |
0.019 |
0.012 |
1.873 |
| HMC |
30 |
0.097 |
0.024 |
0.011 |
6.666 |
| SMC |
2 |
0.018 |
0.022 |
0.012 |
-0.351 |
| SMC |
3 |
0.018 |
0.019 |
0.016 |
-0.045 |
| SMC |
5 |
0.016 |
0.017 |
0.010 |
-0.072 |
| SMC |
8 |
0.018 |
0.019 |
0.014 |
-0.059 |
| SMC |
15 |
0.020 |
0.019 |
0.012 |
0.044 |
| SMC |
30 |
0.021 |
0.024 |
0.011 |
-0.291 |
| Metro |
2 |
0.147 |
0.022 |
0.012 |
10.408 |
| Metro |
3 |
0.180 |
0.019 |
0.016 |
10.378 |
| Metro |
5 |
0.290 |
0.017 |
0.010 |
27.186 |
| Metro |
8 |
0.364 |
0.019 |
0.014 |
23.958 |
| Metro |
15 |
0.447 |
0.019 |
0.012 |
34.438 |
| Metro |
30 |
0.781 |
0.024 |
0.011 |
68.745 |
| DEMetro_Z |
2 |
0.029 |
0.022 |
0.012 |
0.604 |
| DEMetro_Z |
3 |
0.193 |
0.019 |
0.016 |
11.172 |
| DEMetro_Z |
5 |
6.535 |
0.017 |
0.010 |
648.043 |
| DEMetro_Z |
8 |
7.795 |
0.019 |
0.014 |
540.024 |
| DEMetro_Z |
15 |
9.260 |
0.019 |
0.012 |
743.445 |
| DEMetro_Z |
30 |
11.162 |
0.024 |
0.011 |
1011.243 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.216 |
8.55e-06 |
3.171 |
| HMC |
3 |
2.565 |
0.0132 |
0.790 |
| HMC |
5 |
2.996 |
0.00479 |
1.458 |
| HMC |
8 |
3.675 |
0.000603 |
1.299 |
| HMC |
15 |
5.770 |
2.15e-06 |
4.843 |
| HMC |
30 |
4.283 |
0.000162 |
3.885 |
| SMC |
2 |
2.195 |
0.0329 |
0.751 |
| SMC |
3 |
-1.106 |
0.274 |
-0.294 |
| SMC |
5 |
0.163 |
0.871 |
0.044 |
| SMC |
8 |
0.541 |
0.59 |
0.136 |
| SMC |
15 |
1.552 |
0.127 |
0.522 |
| SMC |
30 |
-1.229 |
0.224 |
-0.278 |
| Metro |
2 |
5.670 |
3.71e-06 |
10.739 |
| Metro |
3 |
5.477 |
5.68e-06 |
6.037 |
| Metro |
5 |
7.901 |
7.48e-09 |
9.583 |
| Metro |
8 |
5.950 |
1.74e-06 |
13.498 |
| Metro |
15 |
8.690 |
1.37e-09 |
30.112 |
| Metro |
30 |
12.453 |
2.81e-13 |
24.165 |
| DEMetro_Z |
2 |
4.953 |
2.06e-05 |
3.399 |
| DEMetro_Z |
3 |
2.391 |
0.0235 |
107.366 |
| DEMetro_Z |
5 |
2.557 |
0.0161 |
3644.017 |
| DEMetro_Z |
8 |
4.880 |
3.54e-05 |
1617.885 |
| DEMetro_Z |
15 |
12.609 |
2.7e-13 |
1860.820 |
| DEMetro_Z |
30 |
14.804 |
4.71e-15 |
978.458 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.796
|
0.000694
|
0.693
|
| HMC_vs_SMC |
1
|
3.540
|
0.00137
|
0.646
|
| HMC_vs_SMC |
2
|
3.146
|
0.00381
|
0.574
|
| HMC_vs_SMC |
3
|
3.495
|
0.00154
|
0.638
|
| HMC_vs_SMC |
4
|
5.070
|
2.09e-05
|
0.926
|
| HMC_vs_SMC |
5
|
4.591
|
7.89e-05
|
0.838
|
| Metro_vs_DEMetro_Z |
0
|
3.548
|
0.00134
|
0.648
|
| Metro_vs_DEMetro_Z |
1
|
-2.244
|
0.0326
|
-0.410
|
| Metro_vs_DEMetro_Z |
2
|
-2.550
|
0.0163
|
-0.465
|
| Metro_vs_DEMetro_Z |
3
|
-4.845
|
3.9e-05
|
-0.885
|
| Metro_vs_DEMetro_Z |
4
|
-12.418
|
3.93e-13
|
-2.267
|
| Metro_vs_DEMetro_Z |
5
|
-14.323
|
1.1e-14
|
-2.615
|
| HMC_vs_Metro |
0
|
-3.992
|
0.000409
|
-0.729
|
| HMC_vs_Metro |
1
|
-5.048
|
2.22e-05
|
-0.922
|
| HMC_vs_Metro |
2
|
-6.451
|
4.66e-07
|
-1.178
|
| HMC_vs_Metro |
3
|
-5.598
|
4.82e-06
|
-1.022
|
| HMC_vs_Metro |
4
|
-6.869
|
1.52e-07
|
-1.254
|
| HMC_vs_Metro |
5
|
-11.833
|
1.27e-12
|
-2.160
|
| HMC_vs_DEMetro_Z |
0
|
-0.267
|
0.791
|
-0.049
|
| HMC_vs_DEMetro_Z |
1
|
-2.375
|
0.0244
|
-0.434
|
| HMC_vs_DEMetro_Z |
2
|
-2.555
|
0.0161
|
-0.467
|
| HMC_vs_DEMetro_Z |
3
|
-4.877
|
3.57e-05
|
-0.890
|
| HMC_vs_DEMetro_Z |
4
|
-12.596
|
2.77e-13
|
-2.300
|
| HMC_vs_DEMetro_Z |
5
|
-14.691
|
5.74e-15
|
-2.682
|
| Metro_vs_SMC |
0
|
5.303
|
1.09e-05
|
0.968
|
| Metro_vs_SMC |
1
|
5.782
|
2.9e-06
|
1.056
|
| Metro_vs_SMC |
2
|
7.687
|
1.78e-08
|
1.403
|
| Metro_vs_SMC |
3
|
5.839
|
2.48e-06
|
1.066
|
| Metro_vs_SMC |
4
|
8.662
|
1.55e-09
|
1.581
|
| Metro_vs_SMC |
5
|
12.751
|
2.04e-13
|
2.328
|
| DEMetro_Z_vs_SMC |
0
|
3.702
|
0.000892
|
0.676
|
| DEMetro_Z_vs_SMC |
1
|
2.397
|
0.0232
|
0.438
|
| DEMetro_Z_vs_SMC |
2
|
2.557
|
0.0161
|
0.467
|
| DEMetro_Z_vs_SMC |
3
|
4.880
|
3.54e-05
|
0.891
|
| DEMetro_Z_vs_SMC |
4
|
12.605
|
2.72e-13
|
2.301
|
| DEMetro_Z_vs_SMC |
5
|
14.804
|
4.71e-15
|
2.703
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.054 |
0.019 |
0.011 |
3.171 |
| HMC |
3 |
0.045 |
0.030 |
0.019 |
0.790 |
| HMC |
5 |
0.051 |
0.028 |
0.015 |
1.458 |
| HMC |
8 |
0.049 |
0.026 |
0.018 |
1.299 |
| HMC |
15 |
0.086 |
0.024 |
0.013 |
4.843 |
| HMC |
30 |
0.113 |
0.029 |
0.022 |
3.885 |
| SMC |
2 |
0.027 |
0.019 |
0.011 |
0.751 |
| SMC |
3 |
0.025 |
0.030 |
0.019 |
-0.294 |
| SMC |
5 |
0.029 |
0.028 |
0.015 |
0.044 |
| SMC |
8 |
0.028 |
0.026 |
0.018 |
0.136 |
| SMC |
15 |
0.031 |
0.024 |
0.013 |
0.522 |
| SMC |
30 |
0.023 |
0.029 |
0.022 |
-0.278 |
| Metro |
2 |
0.138 |
0.019 |
0.011 |
10.739 |
| Metro |
3 |
0.145 |
0.030 |
0.019 |
6.037 |
| Metro |
5 |
0.174 |
0.028 |
0.015 |
9.583 |
| Metro |
8 |
0.265 |
0.026 |
0.018 |
13.498 |
| Metro |
15 |
0.410 |
0.024 |
0.013 |
30.112 |
| Metro |
30 |
0.549 |
0.029 |
0.022 |
24.165 |
| DEMetro_Z |
2 |
0.057 |
0.019 |
0.011 |
3.399 |
| DEMetro_Z |
3 |
2.071 |
0.030 |
0.019 |
107.366 |
| DEMetro_Z |
5 |
55.533 |
0.028 |
0.015 |
3644.017 |
| DEMetro_Z |
8 |
28.737 |
0.026 |
0.018 |
1617.885 |
| DEMetro_Z |
15 |
23.857 |
0.024 |
0.013 |
1860.820 |
| DEMetro_Z |
30 |
21.092 |
0.029 |
0.022 |
978.458 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.863 |
0.000356 |
1.460 |
| HMC |
3 |
2.839 |
0.00625 |
0.777 |
| HMC |
5 |
6.558 |
2.07e-07 |
5.110 |
| HMC |
8 |
5.612 |
2.26e-06 |
3.060 |
| HMC |
15 |
7.199 |
2.5e-08 |
4.639 |
| HMC |
30 |
8.379 |
2.17e-09 |
10.227 |
| SMC |
2 |
-1.082 |
0.284 |
-0.266 |
| SMC |
3 |
-1.038 |
0.304 |
-0.232 |
| SMC |
5 |
0.313 |
0.756 |
0.106 |
| SMC |
8 |
-0.508 |
0.613 |
-0.122 |
| SMC |
15 |
1.241 |
0.22 |
0.348 |
| SMC |
30 |
-0.915 |
0.364 |
-0.267 |
| Metro |
2 |
7.395 |
3.47e-08 |
16.005 |
| Metro |
3 |
8.576 |
1.51e-09 |
13.136 |
| Metro |
5 |
8.968 |
7.22e-10 |
50.841 |
| Metro |
8 |
8.654 |
1.53e-09 |
37.230 |
| Metro |
15 |
9.189 |
4.27e-10 |
58.870 |
| Metro |
30 |
8.127 |
5.79e-09 |
97.540 |
| DEMetro_Z |
2 |
5.298 |
4.1e-06 |
2.232 |
| DEMetro_Z |
3 |
4.550 |
8.75e-05 |
15.490 |
| DEMetro_Z |
5 |
6.731 |
2.19e-07 |
1249.656 |
| DEMetro_Z |
8 |
8.800 |
1.1e-09 |
848.501 |
| DEMetro_Z |
15 |
28.232 |
1.21e-22 |
1178.440 |
| DEMetro_Z |
30 |
36.681 |
7.45e-26 |
1420.617 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
6.288
|
7.25e-07
|
1.148
|
| Metro_vs_DEMetro_Z |
1
|
-0.614
|
0.544
|
-0.112
|
| Metro_vs_DEMetro_Z |
2
|
-6.476
|
4.35e-07
|
-1.182
|
| Metro_vs_DEMetro_Z |
3
|
-8.313
|
3.66e-09
|
-1.518
|
| Metro_vs_DEMetro_Z |
4
|
-25.851
|
1.42e-21
|
-4.720
|
| Metro_vs_DEMetro_Z |
5
|
-35.525
|
1.85e-25
|
-6.486
|
| DEMetro_Z_vs_SMC |
0
|
5.651
|
4.17e-06
|
1.032
|
| DEMetro_Z_vs_SMC |
1
|
4.608
|
7.52e-05
|
0.841
|
| DEMetro_Z_vs_SMC |
2
|
6.734
|
2.17e-07
|
1.229
|
| DEMetro_Z_vs_SMC |
3
|
8.807
|
1.09e-09
|
1.608
|
| DEMetro_Z_vs_SMC |
4
|
28.273
|
1.16e-22
|
5.162
|
| DEMetro_Z_vs_SMC |
5
|
36.722
|
7.23e-26
|
6.704
|
| HMC_vs_DEMetro_Z |
0
|
-1.488
|
0.147
|
-0.272
|
| HMC_vs_DEMetro_Z |
1
|
-4.270
|
0.000192
|
-0.780
|
| HMC_vs_DEMetro_Z |
2
|
-6.691
|
2.44e-07
|
-1.222
|
| HMC_vs_DEMetro_Z |
3
|
-8.767
|
1.2e-09
|
-1.601
|
| HMC_vs_DEMetro_Z |
4
|
-28.272
|
1.16e-22
|
-5.162
|
| HMC_vs_DEMetro_Z |
5
|
-36.478
|
8.74e-26
|
-6.660
|
| HMC_vs_Metro |
0
|
-6.933
|
1.28e-07
|
-1.266
|
| HMC_vs_Metro |
1
|
-8.285
|
3.92e-09
|
-1.513
|
| HMC_vs_Metro |
2
|
-7.842
|
1.2e-08
|
-1.432
|
| HMC_vs_Metro |
3
|
-7.968
|
8.7e-09
|
-1.455
|
| HMC_vs_Metro |
4
|
-8.206
|
4.77e-09
|
-1.498
|
| HMC_vs_Metro |
5
|
-7.428
|
3.48e-08
|
-1.356
|
| HMC_vs_SMC |
0
|
4.943
|
2.97e-05
|
0.902
|
| HMC_vs_SMC |
1
|
4.250
|
0.000202
|
0.776
|
| HMC_vs_SMC |
2
|
6.417
|
5.11e-07
|
1.172
|
| HMC_vs_SMC |
3
|
6.177
|
9.8e-07
|
1.128
|
| HMC_vs_SMC |
4
|
6.404
|
5.29e-07
|
1.169
|
| HMC_vs_SMC |
5
|
8.478
|
2.43e-09
|
1.548
|
| Metro_vs_SMC |
0
|
7.547
|
2.55e-08
|
1.378
|
| Metro_vs_SMC |
1
|
8.827
|
1.03e-09
|
1.612
|
| Metro_vs_SMC |
2
|
9.004
|
6.75e-10
|
1.644
|
| Metro_vs_SMC |
3
|
8.625
|
1.69e-09
|
1.575
|
| Metro_vs_SMC |
4
|
9.164
|
4.6e-10
|
1.673
|
| Metro_vs_SMC |
5
|
8.154
|
5.44e-09
|
1.489
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.039 |
0.027 |
0.008 |
1.460 |
| HMC |
3 |
0.036 |
0.028 |
0.011 |
0.777 |
| HMC |
5 |
0.047 |
0.023 |
0.005 |
5.110 |
| HMC |
8 |
0.051 |
0.025 |
0.008 |
3.060 |
| HMC |
15 |
0.055 |
0.024 |
0.007 |
4.639 |
| HMC |
30 |
0.095 |
0.028 |
0.007 |
10.227 |
| SMC |
2 |
0.025 |
0.027 |
0.008 |
-0.266 |
| SMC |
3 |
0.025 |
0.028 |
0.011 |
-0.232 |
| SMC |
5 |
0.024 |
0.023 |
0.005 |
0.106 |
| SMC |
8 |
0.024 |
0.025 |
0.008 |
-0.122 |
| SMC |
15 |
0.026 |
0.024 |
0.007 |
0.348 |
| SMC |
30 |
0.026 |
0.028 |
0.007 |
-0.267 |
| Metro |
2 |
0.156 |
0.027 |
0.008 |
16.005 |
| Metro |
3 |
0.170 |
0.028 |
0.011 |
13.136 |
| Metro |
5 |
0.260 |
0.023 |
0.005 |
50.841 |
| Metro |
8 |
0.335 |
0.025 |
0.008 |
37.230 |
| Metro |
15 |
0.420 |
0.024 |
0.007 |
58.870 |
| Metro |
30 |
0.670 |
0.028 |
0.007 |
97.540 |
| DEMetro_Z |
2 |
0.045 |
0.027 |
0.008 |
2.232 |
| DEMetro_Z |
3 |
0.196 |
0.028 |
0.011 |
15.490 |
| DEMetro_Z |
5 |
5.850 |
0.023 |
0.005 |
1249.656 |
| DEMetro_Z |
8 |
7.088 |
0.025 |
0.008 |
848.501 |
| DEMetro_Z |
15 |
7.963 |
0.024 |
0.007 |
1178.440 |
| DEMetro_Z |
30 |
9.387 |
0.028 |
0.007 |
1420.617 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
4.214 |
0.000129 |
1.750 |
| HMC |
3 |
3.387 |
0.00129 |
0.960 |
| HMC |
5 |
5.724 |
2.06e-06 |
3.871 |
| HMC |
8 |
5.823 |
7.6e-07 |
2.503 |
| HMC |
15 |
7.666 |
5.04e-09 |
4.424 |
| HMC |
30 |
8.582 |
1.06e-09 |
8.440 |
| SMC |
2 |
-0.830 |
0.41 |
-0.217 |
| SMC |
3 |
-0.735 |
0.466 |
-0.165 |
| SMC |
5 |
0.317 |
0.753 |
0.116 |
| SMC |
8 |
-0.637 |
0.527 |
-0.140 |
| SMC |
15 |
1.257 |
0.214 |
0.335 |
| SMC |
30 |
-0.087 |
0.931 |
-0.027 |
| Metro |
2 |
8.127 |
5.01e-09 |
14.907 |
| Metro |
3 |
8.756 |
8.84e-10 |
11.567 |
| Metro |
5 |
9.968 |
6.78e-11 |
39.470 |
| Metro |
8 |
10.126 |
4.53e-11 |
28.900 |
| Metro |
15 |
11.314 |
3.58e-12 |
51.993 |
| Metro |
30 |
10.282 |
3.45e-11 |
81.420 |
| DEMetro_Z |
2 |
4.335 |
9.63e-05 |
1.966 |
| DEMetro_Z |
3 |
9.001 |
6.09e-11 |
4.475 |
| DEMetro_Z |
5 |
17.270 |
8.3e-17 |
186.648 |
| DEMetro_Z |
8 |
36.542 |
6.72e-26 |
133.069 |
| DEMetro_Z |
15 |
98.534 |
9.79e-39 |
190.524 |
| DEMetro_Z |
30 |
78.067 |
1.36e-35 |
185.762 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.534
|
9.24e-05
|
0.828
|
| DEMetro_Z_vs_SMC |
1
|
10.975
|
7.67e-12
|
2.004
|
| DEMetro_Z_vs_SMC |
2
|
17.282
|
8.25e-17
|
3.155
|
| DEMetro_Z_vs_SMC |
3
|
36.937
|
6.13e-26
|
6.744
|
| DEMetro_Z_vs_SMC |
4
|
98.570
|
3.43e-38
|
17.996
|
| DEMetro_Z_vs_SMC |
5
|
76.700
|
4.82e-35
|
14.003
|
| HMC_vs_Metro |
0
|
-7.306
|
4.78e-08
|
-1.334
|
| HMC_vs_Metro |
1
|
-8.473
|
2.46e-09
|
-1.547
|
| HMC_vs_Metro |
2
|
-8.690
|
1.44e-09
|
-1.587
|
| HMC_vs_Metro |
3
|
-9.229
|
3.95e-10
|
-1.685
|
| HMC_vs_Metro |
4
|
-9.923
|
7.87e-11
|
-1.812
|
| HMC_vs_Metro |
5
|
-9.536
|
1.92e-10
|
-1.741
|
| Metro_vs_DEMetro_Z |
0
|
6.847
|
1.61e-07
|
1.250
|
| Metro_vs_DEMetro_Z |
1
|
5.140
|
1.72e-05
|
0.938
|
| Metro_vs_DEMetro_Z |
2
|
-13.477
|
5.14e-14
|
-2.461
|
| Metro_vs_DEMetro_Z |
3
|
-20.260
|
1.16e-18
|
-3.699
|
| Metro_vs_DEMetro_Z |
4
|
-26.309
|
8.69e-22
|
-4.803
|
| Metro_vs_DEMetro_Z |
5
|
-13.596
|
4.12e-14
|
-2.482
|
| HMC_vs_SMC |
0
|
4.793
|
4.51e-05
|
0.875
|
| HMC_vs_SMC |
1
|
4.508
|
9.92e-05
|
0.823
|
| HMC_vs_SMC |
2
|
5.939
|
1.88e-06
|
1.084
|
| HMC_vs_SMC |
3
|
7.370
|
4.05e-08
|
1.346
|
| HMC_vs_SMC |
4
|
7.091
|
8.42e-08
|
1.295
|
| HMC_vs_SMC |
5
|
8.292
|
3.85e-09
|
1.514
|
| Metro_vs_SMC |
0
|
8.257
|
4.2e-09
|
1.507
|
| Metro_vs_SMC |
1
|
9.021
|
6.48e-10
|
1.647
|
| Metro_vs_SMC |
2
|
10.028
|
6.19e-11
|
1.831
|
| Metro_vs_SMC |
3
|
10.046
|
5.95e-11
|
1.834
|
| Metro_vs_SMC |
4
|
11.231
|
4.45e-12
|
2.050
|
| Metro_vs_SMC |
5
|
10.316
|
3.25e-11
|
1.883
|
| HMC_vs_DEMetro_Z |
0
|
-0.379
|
0.707
|
-0.069
|
| HMC_vs_DEMetro_Z |
1
|
-6.495
|
4.14e-07
|
-1.186
|
| HMC_vs_DEMetro_Z |
2
|
-16.699
|
2.05e-16
|
-3.049
|
| HMC_vs_DEMetro_Z |
3
|
-36.771
|
6.96e-26
|
-6.713
|
| HMC_vs_DEMetro_Z |
4
|
-99.151
|
2.89e-38
|
-18.102
|
| HMC_vs_DEMetro_Z |
5
|
-73.695
|
1.53e-34
|
-13.455
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.023 |
0.014 |
0.005 |
1.750 |
| HMC |
3 |
0.022 |
0.015 |
0.007 |
0.960 |
| HMC |
5 |
0.026 |
0.013 |
0.003 |
3.871 |
| HMC |
8 |
0.030 |
0.014 |
0.006 |
2.503 |
| HMC |
15 |
0.035 |
0.014 |
0.005 |
4.424 |
| HMC |
30 |
0.059 |
0.016 |
0.005 |
8.440 |
| SMC |
2 |
0.013 |
0.014 |
0.005 |
-0.217 |
| SMC |
3 |
0.014 |
0.015 |
0.007 |
-0.165 |
| SMC |
5 |
0.013 |
0.013 |
0.003 |
0.116 |
| SMC |
8 |
0.013 |
0.014 |
0.006 |
-0.140 |
| SMC |
15 |
0.015 |
0.014 |
0.005 |
0.335 |
| SMC |
30 |
0.016 |
0.016 |
0.005 |
-0.027 |
| Metro |
2 |
0.087 |
0.014 |
0.005 |
14.907 |
| Metro |
3 |
0.100 |
0.015 |
0.007 |
11.567 |
| Metro |
5 |
0.148 |
0.013 |
0.003 |
39.470 |
| Metro |
8 |
0.200 |
0.014 |
0.006 |
28.900 |
| Metro |
15 |
0.263 |
0.014 |
0.005 |
51.993 |
| Metro |
30 |
0.428 |
0.016 |
0.005 |
81.420 |
| DEMetro_Z |
2 |
0.024 |
0.014 |
0.005 |
1.966 |
| DEMetro_Z |
3 |
0.048 |
0.015 |
0.007 |
4.475 |
| DEMetro_Z |
5 |
0.652 |
0.013 |
0.003 |
186.648 |
| DEMetro_Z |
8 |
0.872 |
0.014 |
0.006 |
133.069 |
| DEMetro_Z |
15 |
0.927 |
0.014 |
0.005 |
190.524 |
| DEMetro_Z |
30 |
0.956 |
0.016 |
0.005 |
185.762 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_heavy_Tails
(MvStudentT,
dimension,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.458 |
0.648 |
0.135 |
| HMC |
3 |
0.257 |
0.798 |
0.070 |
| HMC |
5 |
-1.326 |
0.191 |
-0.293 |
| HMC |
8 |
-0.542 |
0.59 |
-0.154 |
| HMC |
15 |
0.190 |
0.85 |
0.045 |
| HMC |
30 |
2.278 |
0.0297 |
2.172 |
| SMC |
2 |
-0.886 |
0.38 |
-0.203 |
| SMC |
3 |
1.720 |
0.0908 |
0.429 |
| SMC |
5 |
6.877 |
9.83e-09 |
2.322 |
| SMC |
8 |
9.083 |
3.83e-10 |
11.549 |
| SMC |
15 |
10.284 |
1.53e-14 |
2.453 |
| SMC |
30 |
23.248 |
9.2e-25 |
10.558 |
| Metro |
2 |
3.132 |
0.00361 |
2.184 |
| Metro |
3 |
2.972 |
0.00549 |
2.129 |
| Metro |
5 |
3.267 |
0.00199 |
0.706 |
| Metro |
8 |
5.129 |
1.39e-05 |
4.358 |
| Metro |
15 |
3.833 |
0.000421 |
1.623 |
| Metro |
30 |
7.255 |
4.84e-08 |
13.064 |
| DEMetro_Z |
2 |
4.667 |
2.41e-05 |
1.602 |
| DEMetro_Z |
3 |
3.847 |
0.000605 |
31.759 |
| DEMetro_Z |
5 |
6.579 |
3.29e-07 |
72.143 |
| DEMetro_Z |
8 |
6.315 |
6.73e-07 |
110.351 |
| DEMetro_Z |
15 |
20.842 |
4.44e-19 |
64.809 |
| DEMetro_Z |
30 |
19.763 |
2.26e-18 |
407.501 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-4.435
|
0.000121
|
-0.810
|
| HMC_vs_DEMetro_Z |
1
|
-3.816
|
0.000657
|
-0.697
|
| HMC_vs_DEMetro_Z |
2
|
-6.600
|
3.12e-07
|
-1.205
|
| HMC_vs_DEMetro_Z |
3
|
-6.336
|
6.36e-07
|
-1.157
|
| HMC_vs_DEMetro_Z |
4
|
-21.053
|
4.07e-19
|
-3.844
|
| HMC_vs_DEMetro_Z |
5
|
-19.922
|
1.83e-18
|
-3.637
|
| Metro_vs_SMC |
0
|
3.511
|
0.00148
|
0.641
|
| Metro_vs_SMC |
1
|
2.384
|
0.0239
|
0.435
|
| Metro_vs_SMC |
2
|
-5.329
|
1.02e-05
|
-0.973
|
| Metro_vs_SMC |
3
|
-4.301
|
0.000176
|
-0.785
|
| Metro_vs_SMC |
4
|
-1.990
|
0.0561
|
-0.363
|
| Metro_vs_SMC |
5
|
1.474
|
0.151
|
0.269
|
| Metro_vs_DEMetro_Z |
0
|
0.825
|
0.416
|
0.151
|
| Metro_vs_DEMetro_Z |
1
|
-3.546
|
0.00135
|
-0.647
|
| Metro_vs_DEMetro_Z |
2
|
-6.531
|
3.75e-07
|
-1.192
|
| Metro_vs_DEMetro_Z |
3
|
-6.060
|
1.35e-06
|
-1.106
|
| Metro_vs_DEMetro_Z |
4
|
-20.038
|
1.56e-18
|
-3.658
|
| Metro_vs_DEMetro_Z |
5
|
-19.157
|
5.26e-18
|
-3.498
|
| HMC_vs_Metro |
0
|
-2.899
|
0.00707
|
-0.529
|
| HMC_vs_Metro |
1
|
-2.963
|
0.00602
|
-0.541
|
| HMC_vs_Metro |
2
|
-6.852
|
1.59e-07
|
-1.251
|
| HMC_vs_Metro |
3
|
-5.098
|
1.93e-05
|
-0.931
|
| HMC_vs_Metro |
4
|
-3.627
|
0.00109
|
-0.662
|
| HMC_vs_Metro |
5
|
-5.395
|
8.46e-06
|
-0.985
|
| HMC_vs_SMC |
0
|
1.261
|
0.217
|
0.230
|
| HMC_vs_SMC |
1
|
-1.248
|
0.222
|
-0.228
|
| HMC_vs_SMC |
2
|
-8.027
|
7.48e-09
|
-1.466
|
| HMC_vs_SMC |
3
|
-9.030
|
6.33e-10
|
-1.649
|
| HMC_vs_SMC |
4
|
-11.417
|
3.01e-12
|
-2.084
|
| HMC_vs_SMC |
5
|
-8.192
|
4.94e-09
|
-1.496
|
| DEMetro_Z_vs_SMC |
0
|
5.623
|
4.51e-06
|
1.027
|
| DEMetro_Z_vs_SMC |
1
|
3.808
|
0.000671
|
0.695
|
| DEMetro_Z_vs_SMC |
2
|
6.375
|
5.73e-07
|
1.164
|
| DEMetro_Z_vs_SMC |
3
|
5.595
|
4.86e-06
|
1.022
|
| DEMetro_Z_vs_SMC |
4
|
19.967
|
1.72e-18
|
3.646
|
| DEMetro_Z_vs_SMC |
5
|
19.230
|
4.74e-18
|
3.511
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.070 |
0.065 |
0.042 |
0.135 |
| HMC |
3 |
0.069 |
0.067 |
0.033 |
0.070 |
| HMC |
5 |
0.059 |
0.071 |
0.043 |
-0.293 |
| HMC |
8 |
0.057 |
0.060 |
0.018 |
-0.154 |
| HMC |
15 |
0.078 |
0.076 |
0.059 |
0.045 |
| HMC |
30 |
0.095 |
0.067 |
0.013 |
2.172 |
| SMC |
2 |
0.056 |
0.065 |
0.042 |
-0.203 |
| SMC |
3 |
0.081 |
0.067 |
0.033 |
0.429 |
| SMC |
5 |
0.172 |
0.071 |
0.043 |
2.322 |
| SMC |
8 |
0.262 |
0.060 |
0.018 |
11.549 |
| SMC |
15 |
0.221 |
0.076 |
0.059 |
2.453 |
| SMC |
30 |
0.204 |
0.067 |
0.013 |
10.558 |
| Metro |
2 |
0.156 |
0.065 |
0.042 |
2.184 |
| Metro |
3 |
0.137 |
0.067 |
0.033 |
2.129 |
| Metro |
5 |
0.102 |
0.071 |
0.043 |
0.706 |
| Metro |
8 |
0.136 |
0.060 |
0.018 |
4.358 |
| Metro |
15 |
0.172 |
0.076 |
0.059 |
1.623 |
| Metro |
30 |
0.237 |
0.067 |
0.013 |
13.064 |
| DEMetro_Z |
2 |
0.132 |
0.065 |
0.042 |
1.602 |
| DEMetro_Z |
3 |
1.114 |
0.067 |
0.033 |
31.759 |
| DEMetro_Z |
5 |
3.192 |
0.071 |
0.043 |
72.143 |
| DEMetro_Z |
8 |
1.991 |
0.060 |
0.018 |
110.351 |
| DEMetro_Z |
15 |
3.926 |
0.076 |
0.059 |
64.809 |
| DEMetro_Z |
30 |
5.369 |
0.067 |
0.013 |
407.501 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.083 |
0.934 |
0.031 |
| HMC |
3 |
1.779 |
0.0833 |
0.879 |
| HMC |
5 |
-1.584 |
0.123 |
-0.297 |
| HMC |
8 |
-0.898 |
0.374 |
-0.185 |
| HMC |
15 |
-1.152 |
0.259 |
-0.210 |
| HMC |
30 |
1.238 |
0.225 |
1.304 |
| SMC |
2 |
-2.065 |
0.0468 |
-0.391 |
| SMC |
3 |
1.604 |
0.117 |
0.757 |
| SMC |
5 |
-0.763 |
0.451 |
-0.140 |
| SMC |
8 |
15.252 |
5.87e-22 |
3.920 |
| SMC |
15 |
1.533 |
0.136 |
0.281 |
| SMC |
30 |
48.527 |
1.72e-42 |
16.968 |
| Metro |
2 |
-0.742 |
0.462 |
-0.155 |
| Metro |
3 |
1.583 |
0.122 |
0.797 |
| Metro |
5 |
-1.937 |
0.0625 |
-0.354 |
| Metro |
8 |
0.357 |
0.722 |
0.090 |
| Metro |
15 |
-0.772 |
0.446 |
-0.145 |
| Metro |
30 |
2.491 |
0.0185 |
3.746 |
| DEMetro_Z |
2 |
-1.657 |
0.107 |
-0.315 |
| DEMetro_Z |
3 |
1.954 |
0.0605 |
68.481 |
| DEMetro_Z |
5 |
4.194 |
0.000233 |
13.108 |
| DEMetro_Z |
8 |
4.484 |
0.000106 |
19.988 |
| DEMetro_Z |
15 |
10.355 |
2.21e-14 |
3.176 |
| DEMetro_Z |
30 |
15.218 |
2.18e-15 |
70.078 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.268
|
0.215
|
0.231
|
| HMC_vs_SMC |
1
|
0.428
|
0.672
|
0.078
|
| HMC_vs_SMC |
2
|
-3.487
|
0.00158
|
-0.637
|
| HMC_vs_SMC |
3
|
-21.466
|
2.39e-19
|
-3.919
|
| HMC_vs_SMC |
4
|
-36.616
|
7.85e-26
|
-6.685
|
| HMC_vs_SMC |
5
|
-18.867
|
7.92e-18
|
-3.445
|
| Metro_vs_DEMetro_Z |
0
|
1.611
|
0.118
|
0.294
|
| Metro_vs_DEMetro_Z |
1
|
-1.928
|
0.0637
|
-0.352
|
| Metro_vs_DEMetro_Z |
2
|
-4.312
|
0.00017
|
-0.787
|
| Metro_vs_DEMetro_Z |
3
|
-4.435
|
0.000122
|
-0.810
|
| Metro_vs_DEMetro_Z |
4
|
-12.720
|
2.17e-13
|
-2.322
|
| Metro_vs_DEMetro_Z |
5
|
-14.510
|
7.89e-15
|
-2.649
|
| HMC_vs_Metro |
0
|
0.531
|
0.6
|
0.097
|
| HMC_vs_Metro |
1
|
0.312
|
0.757
|
0.057
|
| HMC_vs_Metro |
2
|
1.365
|
0.183
|
0.249
|
| HMC_vs_Metro |
3
|
-1.750
|
0.0907
|
-0.320
|
| HMC_vs_Metro |
4
|
-1.410
|
0.169
|
-0.258
|
| HMC_vs_Metro |
5
|
-2.024
|
0.0523
|
-0.370
|
| HMC_vs_DEMetro_Z |
0
|
1.034
|
0.31
|
0.189
|
| HMC_vs_DEMetro_Z |
1
|
-1.925
|
0.0641
|
-0.351
|
| HMC_vs_DEMetro_Z |
2
|
-4.286
|
0.000183
|
-0.783
|
| HMC_vs_DEMetro_Z |
3
|
-4.512
|
9.84e-05
|
-0.824
|
| HMC_vs_DEMetro_Z |
4
|
-13.718
|
3.29e-14
|
-2.504
|
| HMC_vs_DEMetro_Z |
5
|
-15.517
|
1.4e-15
|
-2.833
|
| Metro_vs_SMC |
0
|
2.350
|
0.0258
|
0.429
|
| Metro_vs_SMC |
1
|
0.110
|
0.913
|
0.020
|
| Metro_vs_SMC |
2
|
-9.735
|
1.21e-10
|
-1.777
|
| Metro_vs_SMC |
3
|
-15.360
|
1.82e-15
|
-2.804
|
| Metro_vs_SMC |
4
|
-8.747
|
1.26e-09
|
-1.597
|
| Metro_vs_SMC |
5
|
-9.577
|
1.74e-10
|
-1.749
|
| DEMetro_Z_vs_SMC |
0
|
2.304
|
0.0286
|
0.421
|
| DEMetro_Z_vs_SMC |
1
|
1.929
|
0.0636
|
0.352
|
| DEMetro_Z_vs_SMC |
2
|
4.244
|
0.000206
|
0.775
|
| DEMetro_Z_vs_SMC |
3
|
3.615
|
0.00112
|
0.660
|
| DEMetro_Z_vs_SMC |
4
|
11.902
|
1.11e-12
|
2.173
|
| DEMetro_Z_vs_SMC |
5
|
11.624
|
1.95e-12
|
2.122
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
9.559 |
9.112 |
14.240 |
0.031 |
| HMC |
3 |
6.978 |
4.160 |
3.204 |
0.879 |
| HMC |
5 |
6.017 |
17.558 |
38.901 |
-0.297 |
| HMC |
8 |
3.904 |
5.290 |
7.509 |
-0.185 |
| HMC |
15 |
4.516 |
33.738 |
138.861 |
-0.210 |
| HMC |
30 |
12.709 |
5.218 |
5.743 |
1.304 |
| SMC |
2 |
3.545 |
9.112 |
14.240 |
-0.391 |
| SMC |
3 |
6.586 |
4.160 |
3.204 |
0.757 |
| SMC |
5 |
12.110 |
17.558 |
38.901 |
-0.140 |
| SMC |
8 |
34.726 |
5.290 |
7.509 |
3.920 |
| SMC |
15 |
72.691 |
33.738 |
138.861 |
0.281 |
| SMC |
30 |
102.675 |
5.218 |
5.743 |
16.968 |
| Metro |
2 |
6.906 |
9.112 |
14.240 |
-0.155 |
| Metro |
3 |
6.714 |
4.160 |
3.204 |
0.797 |
| Metro |
5 |
3.775 |
17.558 |
38.901 |
-0.354 |
| Metro |
8 |
5.968 |
5.290 |
7.509 |
0.090 |
| Metro |
15 |
13.581 |
33.738 |
138.861 |
-0.145 |
| Metro |
30 |
26.734 |
5.218 |
5.743 |
3.746 |
| DEMetro_Z |
2 |
4.632 |
9.112 |
14.240 |
-0.315 |
| DEMetro_Z |
3 |
223.595 |
4.160 |
3.204 |
68.481 |
| DEMetro_Z |
5 |
527.482 |
17.558 |
38.901 |
13.108 |
| DEMetro_Z |
8 |
155.377 |
5.290 |
7.509 |
19.988 |
| DEMetro_Z |
15 |
474.759 |
33.738 |
138.861 |
3.176 |
| DEMetro_Z |
30 |
407.712 |
5.218 |
5.743 |
70.078 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.468 |
0.0183 |
1.261 |
| HMC |
3 |
4.560 |
5.17e-05 |
2.230 |
| HMC |
5 |
2.262 |
0.0299 |
1.288 |
| HMC |
8 |
3.466 |
0.0014 |
1.987 |
| HMC |
15 |
3.162 |
0.00286 |
1.258 |
| HMC |
30 |
4.800 |
4.32e-05 |
11.925 |
| SMC |
2 |
-0.073 |
0.942 |
-0.017 |
| SMC |
3 |
7.045 |
7.18e-08 |
8.145 |
| SMC |
5 |
22.328 |
2.62e-20 |
29.214 |
| SMC |
8 |
35.919 |
1.12e-25 |
137.443 |
| SMC |
15 |
68.811 |
1.35e-34 |
95.580 |
| SMC |
30 |
156.745 |
1.79e-44 |
364.345 |
| Metro |
2 |
4.852 |
2.93e-05 |
3.644 |
| Metro |
3 |
5.598 |
4.29e-06 |
7.678 |
| Metro |
5 |
6.731 |
1.6e-08 |
2.250 |
| Metro |
8 |
4.607 |
7.21e-05 |
7.742 |
| Metro |
15 |
3.655 |
0.000991 |
6.722 |
| Metro |
30 |
5.691 |
3.73e-06 |
55.865 |
| DEMetro_Z |
2 |
8.865 |
4.66e-11 |
3.868 |
| DEMetro_Z |
3 |
5.079 |
2.04e-05 |
153.234 |
| DEMetro_Z |
5 |
8.395 |
2.98e-09 |
201.625 |
| DEMetro_Z |
8 |
9.086 |
5.54e-10 |
241.537 |
| DEMetro_Z |
15 |
29.058 |
5.23e-23 |
260.038 |
| DEMetro_Z |
30 |
33.931 |
6.77e-25 |
742.551 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.247
|
0.807
|
-0.045
|
| Metro_vs_DEMetro_Z |
1
|
-4.813
|
4.27e-05
|
-0.879
|
| Metro_vs_DEMetro_Z |
2
|
-8.309
|
3.69e-09
|
-1.517
|
| Metro_vs_DEMetro_Z |
3
|
-8.676
|
1.49e-09
|
-1.584
|
| Metro_vs_DEMetro_Z |
4
|
-27.551
|
2.4e-22
|
-5.030
|
| Metro_vs_DEMetro_Z |
5
|
-30.035
|
2.13e-23
|
-5.484
|
| DEMetro_Z_vs_SMC |
0
|
9.223
|
4e-10
|
1.684
|
| DEMetro_Z_vs_SMC |
1
|
4.769
|
4.82e-05
|
0.871
|
| DEMetro_Z_vs_SMC |
2
|
7.109
|
8.02e-08
|
1.298
|
| DEMetro_Z_vs_SMC |
3
|
3.923
|
0.000492
|
0.716
|
| DEMetro_Z_vs_SMC |
4
|
19.016
|
6.42e-18
|
3.472
|
| DEMetro_Z_vs_SMC |
5
|
17.371
|
7.21e-17
|
3.171
|
| HMC_vs_DEMetro_Z |
0
|
-4.134
|
0.000277
|
-0.755
|
| HMC_vs_DEMetro_Z |
1
|
-5.002
|
2.53e-05
|
-0.913
|
| HMC_vs_DEMetro_Z |
2
|
-8.321
|
3.58e-09
|
-1.519
|
| HMC_vs_DEMetro_Z |
3
|
-9.031
|
6.33e-10
|
-1.649
|
| HMC_vs_DEMetro_Z |
4
|
-29.019
|
5.6e-23
|
-5.298
|
| HMC_vs_DEMetro_Z |
5
|
-32.977
|
1.52e-24
|
-6.021
|
| HMC_vs_Metro |
0
|
-2.680
|
0.012
|
-0.489
|
| HMC_vs_Metro |
1
|
-4.292
|
0.00018
|
-0.784
|
| HMC_vs_Metro |
2
|
-1.635
|
0.113
|
-0.298
|
| HMC_vs_Metro |
3
|
-3.161
|
0.00367
|
-0.577
|
| HMC_vs_Metro |
4
|
-2.849
|
0.00798
|
-0.520
|
| HMC_vs_Metro |
5
|
-4.253
|
0.000201
|
-0.776
|
| HMC_vs_SMC |
0
|
2.541
|
0.0167
|
0.464
|
| HMC_vs_SMC |
1
|
-4.635
|
7e-05
|
-0.846
|
| HMC_vs_SMC |
2
|
-21.375
|
2.69e-19
|
-3.903
|
| HMC_vs_SMC |
3
|
-34.677
|
3.68e-25
|
-6.331
|
| HMC_vs_SMC |
4
|
-63.978
|
8.99e-33
|
-11.681
|
| HMC_vs_SMC |
5
|
-102.768
|
1.03e-38
|
-18.763
|
| Metro_vs_SMC |
0
|
4.742
|
5.19e-05
|
0.866
|
| Metro_vs_SMC |
1
|
-0.262
|
0.795
|
-0.048
|
| Metro_vs_SMC |
2
|
-20.552
|
7.84e-19
|
-3.752
|
| Metro_vs_SMC |
3
|
-32.468
|
2.37e-24
|
-5.928
|
| Metro_vs_SMC |
4
|
-41.885
|
1.71e-27
|
-7.647
|
| Metro_vs_SMC |
5
|
-31.634
|
4.94e-24
|
-5.775
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.168 |
0.124 |
0.035 |
1.261 |
| HMC |
3 |
0.154 |
0.115 |
0.018 |
2.230 |
| HMC |
5 |
0.176 |
0.126 |
0.039 |
1.288 |
| HMC |
8 |
0.155 |
0.113 |
0.021 |
1.987 |
| HMC |
15 |
0.204 |
0.136 |
0.054 |
1.258 |
| HMC |
30 |
0.338 |
0.118 |
0.018 |
11.925 |
| SMC |
2 |
0.123 |
0.124 |
0.035 |
-0.017 |
| SMC |
3 |
0.258 |
0.115 |
0.018 |
8.145 |
| SMC |
5 |
1.264 |
0.126 |
0.039 |
29.214 |
| SMC |
8 |
3.008 |
0.113 |
0.021 |
137.443 |
| SMC |
15 |
5.321 |
0.136 |
0.054 |
95.580 |
| SMC |
30 |
6.844 |
0.118 |
0.018 |
364.345 |
| Metro |
2 |
0.251 |
0.124 |
0.035 |
3.644 |
| Metro |
3 |
0.250 |
0.115 |
0.018 |
7.678 |
| Metro |
5 |
0.214 |
0.126 |
0.039 |
2.250 |
| Metro |
8 |
0.276 |
0.113 |
0.021 |
7.742 |
| Metro |
15 |
0.500 |
0.136 |
0.054 |
6.722 |
| Metro |
30 |
1.149 |
0.118 |
0.018 |
55.865 |
| DEMetro_Z |
2 |
0.259 |
0.124 |
0.035 |
3.868 |
| DEMetro_Z |
3 |
2.804 |
0.115 |
0.018 |
153.234 |
| DEMetro_Z |
5 |
7.982 |
0.126 |
0.039 |
201.625 |
| DEMetro_Z |
8 |
5.200 |
0.113 |
0.021 |
241.537 |
| DEMetro_Z |
15 |
14.243 |
0.136 |
0.054 |
260.038 |
| DEMetro_Z |
30 |
13.826 |
0.118 |
0.018 |
742.551 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.862 |
0.000298 |
1.131 |
| HMC |
3 |
2.399 |
0.0222 |
1.654 |
| HMC |
5 |
3.158 |
0.00359 |
3.974 |
| HMC |
8 |
3.444 |
0.00171 |
4.789 |
| HMC |
15 |
4.317 |
0.000166 |
12.414 |
| HMC |
30 |
5.178 |
1.53e-05 |
23.104 |
| SMC |
2 |
2.537 |
0.0144 |
0.870 |
| SMC |
3 |
8.189 |
3.77e-09 |
11.045 |
| SMC |
5 |
35.088 |
1.84e-25 |
97.363 |
| SMC |
8 |
69.912 |
2.99e-34 |
152.941 |
| SMC |
15 |
144.383 |
2.92e-44 |
197.963 |
| SMC |
30 |
152.964 |
1.75e-45 |
180.136 |
| Metro |
2 |
7.089 |
2.38e-08 |
3.835 |
| Metro |
3 |
8.539 |
7.04e-10 |
6.047 |
| Metro |
5 |
8.966 |
5.3e-10 |
12.011 |
| Metro |
8 |
6.798 |
1.68e-07 |
13.840 |
| Metro |
15 |
6.590 |
3.16e-07 |
34.086 |
| Metro |
30 |
10.173 |
4.4e-11 |
73.055 |
| DEMetro_Z |
2 |
9.219 |
1.21e-10 |
6.660 |
| DEMetro_Z |
3 |
10.521 |
2e-11 |
54.324 |
| DEMetro_Z |
5 |
27.993 |
1.45e-22 |
175.522 |
| DEMetro_Z |
8 |
28.865 |
6.07e-23 |
171.304 |
| DEMetro_Z |
15 |
83.035 |
2.8e-36 |
233.126 |
| DEMetro_Z |
30 |
79.217 |
1.11e-35 |
223.737 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
6.807
|
1.79e-07
|
1.243
|
| DEMetro_Z_vs_SMC |
1
|
7.983
|
8.36e-09
|
1.458
|
| DEMetro_Z_vs_SMC |
2
|
11.060
|
6.39e-12
|
2.019
|
| DEMetro_Z_vs_SMC |
3
|
2.819
|
0.00859
|
0.515
|
| DEMetro_Z_vs_SMC |
4
|
12.271
|
5.25e-13
|
2.240
|
| DEMetro_Z_vs_SMC |
5
|
12.659
|
2.45e-13
|
2.311
|
| HMC_vs_Metro |
0
|
-4.851
|
3.84e-05
|
-0.886
|
| HMC_vs_Metro |
1
|
-4.468
|
0.000111
|
-0.816
|
| HMC_vs_Metro |
2
|
-4.454
|
0.000115
|
-0.813
|
| HMC_vs_Metro |
3
|
-3.602
|
0.00116
|
-0.658
|
| HMC_vs_Metro |
4
|
-3.531
|
0.0014
|
-0.645
|
| HMC_vs_Metro |
5
|
-5.872
|
2.27e-06
|
-1.072
|
| Metro_vs_DEMetro_Z |
0
|
-3.739
|
0.000809
|
-0.683
|
| Metro_vs_DEMetro_Z |
1
|
-9.426
|
2.48e-10
|
-1.721
|
| Metro_vs_DEMetro_Z |
2
|
-26.137
|
1.04e-21
|
-4.772
|
| Metro_vs_DEMetro_Z |
3
|
-24.340
|
7.54e-21
|
-4.444
|
| Metro_vs_DEMetro_Z |
4
|
-42.403
|
1.2e-27
|
-7.742
|
| Metro_vs_DEMetro_Z |
5
|
-19.817
|
2.11e-18
|
-3.618
|
| HMC_vs_SMC |
0
|
0.703
|
0.488
|
0.128
|
| HMC_vs_SMC |
1
|
-6.137
|
1.09e-06
|
-1.120
|
| HMC_vs_SMC |
2
|
-33.745
|
7.95e-25
|
-6.161
|
| HMC_vs_SMC |
3
|
-53.724
|
1.37e-30
|
-9.809
|
| HMC_vs_SMC |
4
|
-57.657
|
1.79e-31
|
-10.527
|
| HMC_vs_SMC |
5
|
-37.732
|
3.34e-26
|
-6.889
|
| Metro_vs_SMC |
0
|
4.754
|
5.03e-05
|
0.868
|
| Metro_vs_SMC |
1
|
-3.344
|
0.00229
|
-0.611
|
| Metro_vs_SMC |
2
|
-27.846
|
1.78e-22
|
-5.084
|
| Metro_vs_SMC |
3
|
-50.972
|
6.19e-30
|
-9.306
|
| Metro_vs_SMC |
4
|
-32.794
|
1.78e-24
|
-5.987
|
| Metro_vs_SMC |
5
|
-15.186
|
2.44e-15
|
-2.773
|
| HMC_vs_DEMetro_Z |
0
|
-7.235
|
5.76e-08
|
-1.321
|
| HMC_vs_DEMetro_Z |
1
|
-10.185
|
4.35e-11
|
-1.860
|
| HMC_vs_DEMetro_Z |
2
|
-26.879
|
4.78e-22
|
-4.907
|
| HMC_vs_DEMetro_Z |
3
|
-28.417
|
1.01e-22
|
-5.188
|
| HMC_vs_DEMetro_Z |
4
|
-56.422
|
3.35e-31
|
-10.301
|
| HMC_vs_DEMetro_Z |
5
|
-34.094
|
5.94e-25
|
-6.225
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.020 |
0.015 |
0.005 |
1.131 |
| HMC |
3 |
0.021 |
0.015 |
0.003 |
1.654 |
| HMC |
5 |
0.023 |
0.014 |
0.002 |
3.974 |
| HMC |
8 |
0.026 |
0.015 |
0.002 |
4.789 |
| HMC |
15 |
0.040 |
0.015 |
0.002 |
12.414 |
| HMC |
30 |
0.064 |
0.016 |
0.002 |
23.104 |
| SMC |
2 |
0.019 |
0.015 |
0.005 |
0.870 |
| SMC |
3 |
0.053 |
0.015 |
0.003 |
11.045 |
| SMC |
5 |
0.230 |
0.014 |
0.002 |
97.363 |
| SMC |
8 |
0.361 |
0.015 |
0.002 |
152.941 |
| SMC |
15 |
0.415 |
0.015 |
0.002 |
197.963 |
| SMC |
30 |
0.393 |
0.016 |
0.002 |
180.136 |
| Metro |
2 |
0.032 |
0.015 |
0.005 |
3.835 |
| Metro |
3 |
0.036 |
0.015 |
0.003 |
6.047 |
| Metro |
5 |
0.041 |
0.014 |
0.002 |
12.011 |
| Metro |
8 |
0.046 |
0.015 |
0.002 |
13.840 |
| Metro |
15 |
0.084 |
0.015 |
0.002 |
34.086 |
| Metro |
30 |
0.169 |
0.016 |
0.002 |
73.055 |
| DEMetro_Z |
2 |
0.045 |
0.015 |
0.005 |
6.660 |
| DEMetro_Z |
3 |
0.203 |
0.015 |
0.003 |
54.324 |
| DEMetro_Z |
5 |
0.403 |
0.014 |
0.002 |
175.522 |
| DEMetro_Z |
8 |
0.402 |
0.015 |
0.002 |
171.304 |
| DEMetro_Z |
15 |
0.486 |
0.015 |
0.002 |
233.126 |
| DEMetro_Z |
30 |
0.485 |
0.016 |
0.002 |
223.737 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.003 |
0.32 |
0.290 |
| HMC |
3 |
-1.210 |
0.231 |
-0.281 |
| HMC |
5 |
-1.247 |
0.219 |
-0.253 |
| HMC |
8 |
0.871 |
0.39 |
0.466 |
| HMC |
15 |
1.542 |
0.133 |
1.401 |
| HMC |
30 |
1.805 |
0.0814 |
9.437 |
| SMC |
2 |
-1.225 |
0.226 |
-0.303 |
| SMC |
3 |
1.905 |
0.0632 |
0.718 |
| SMC |
5 |
7.794 |
3.29e-09 |
4.413 |
| SMC |
8 |
11.448 |
2.02e-12 |
18.688 |
| SMC |
15 |
10.569 |
5.76e-13 |
5.037 |
| SMC |
30 |
17.995 |
2.48e-18 |
14.569 |
| Metro |
2 |
2.556 |
0.0155 |
2.083 |
| Metro |
3 |
2.671 |
0.0117 |
2.006 |
| Metro |
5 |
2.214 |
0.0329 |
1.092 |
| Metro |
8 |
2.463 |
0.0199 |
6.283 |
| Metro |
15 |
1.186 |
0.245 |
8.991 |
| Metro |
30 |
6.278 |
5.57e-07 |
6.254 |
| DEMetro_Z |
2 |
4.275 |
0.000129 |
2.214 |
| DEMetro_Z |
3 |
3.411 |
0.00192 |
12.888 |
| DEMetro_Z |
5 |
4.406 |
0.000131 |
29.093 |
| DEMetro_Z |
8 |
6.741 |
2.12e-07 |
50.666 |
| DEMetro_Z |
15 |
12.661 |
2.33e-13 |
60.080 |
| DEMetro_Z |
30 |
24.417 |
6.85e-21 |
381.329 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.842
|
0.000614
|
-0.701
|
| HMC_vs_DEMetro_Z |
1
|
-3.505
|
0.00151
|
-0.640
|
| HMC_vs_DEMetro_Z |
2
|
-4.447
|
0.000118
|
-0.812
|
| HMC_vs_DEMetro_Z |
3
|
-6.593
|
3.17e-07
|
-1.204
|
| HMC_vs_DEMetro_Z |
4
|
-12.306
|
4.9e-13
|
-2.247
|
| HMC_vs_DEMetro_Z |
5
|
-22.023
|
1.19e-19
|
-4.021
|
| Metro_vs_SMC |
0
|
2.955
|
0.00614
|
0.540
|
| Metro_vs_SMC |
1
|
1.501
|
0.144
|
0.274
|
| Metro_vs_SMC |
2
|
-4.500
|
0.000102
|
-0.822
|
| Metro_vs_SMC |
3
|
-4.034
|
0.000365
|
-0.736
|
| Metro_vs_SMC |
4
|
0.514
|
0.611
|
0.094
|
| Metro_vs_SMC |
5
|
-6.638
|
2.81e-07
|
-1.212
|
| Metro_vs_DEMetro_Z |
0
|
-0.129
|
0.898
|
-0.024
|
| Metro_vs_DEMetro_Z |
1
|
-2.745
|
0.0103
|
-0.501
|
| Metro_vs_DEMetro_Z |
2
|
-4.214
|
0.000223
|
-0.769
|
| Metro_vs_DEMetro_Z |
3
|
-5.560
|
5.36e-06
|
-1.015
|
| Metro_vs_DEMetro_Z |
4
|
-5.740
|
3.26e-06
|
-1.048
|
| Metro_vs_DEMetro_Z |
5
|
-23.988
|
1.13e-20
|
-4.380
|
| HMC_vs_Metro |
0
|
-2.186
|
0.0371
|
-0.399
|
| HMC_vs_Metro |
1
|
-3.177
|
0.00352
|
-0.580
|
| HMC_vs_Metro |
2
|
-2.859
|
0.00779
|
-0.522
|
| HMC_vs_Metro |
3
|
-2.202
|
0.0358
|
-0.402
|
| HMC_vs_Metro |
4
|
-0.989
|
0.331
|
-0.181
|
| HMC_vs_Metro |
5
|
0.644
|
0.525
|
0.118
|
| HMC_vs_SMC |
0
|
2.589
|
0.0149
|
0.473
|
| HMC_vs_SMC |
1
|
-2.572
|
0.0155
|
-0.470
|
| HMC_vs_SMC |
2
|
-8.548
|
2.04e-09
|
-1.561
|
| HMC_vs_SMC |
3
|
-11.821
|
1.3e-12
|
-2.158
|
| HMC_vs_SMC |
4
|
-3.998
|
0.000402
|
-0.730
|
| HMC_vs_SMC |
5
|
-0.976
|
0.337
|
-0.178
|
| DEMetro_Z_vs_SMC |
0
|
5.050
|
2.2e-05
|
0.922
|
| DEMetro_Z_vs_SMC |
1
|
3.193
|
0.00338
|
0.583
|
| DEMetro_Z_vs_SMC |
2
|
3.767
|
0.000749
|
0.688
|
| DEMetro_Z_vs_SMC |
3
|
4.103
|
0.000302
|
0.749
|
| DEMetro_Z_vs_SMC |
4
|
11.572
|
2.18e-12
|
2.113
|
| DEMetro_Z_vs_SMC |
5
|
23.338
|
2.41e-20
|
4.261
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.077 |
0.065 |
0.042 |
0.290 |
| HMC |
3 |
0.058 |
0.067 |
0.033 |
-0.281 |
| HMC |
5 |
0.061 |
0.071 |
0.043 |
-0.253 |
| HMC |
8 |
0.068 |
0.060 |
0.018 |
0.466 |
| HMC |
15 |
0.159 |
0.076 |
0.059 |
1.401 |
| HMC |
30 |
0.189 |
0.067 |
0.013 |
9.437 |
| SMC |
2 |
0.052 |
0.065 |
0.042 |
-0.303 |
| SMC |
3 |
0.091 |
0.067 |
0.033 |
0.718 |
| SMC |
5 |
0.262 |
0.071 |
0.043 |
4.413 |
| SMC |
8 |
0.387 |
0.060 |
0.018 |
18.688 |
| SMC |
15 |
0.375 |
0.076 |
0.059 |
5.037 |
| SMC |
30 |
0.256 |
0.067 |
0.013 |
14.569 |
| Metro |
2 |
0.152 |
0.065 |
0.042 |
2.083 |
| Metro |
3 |
0.133 |
0.067 |
0.033 |
2.006 |
| Metro |
5 |
0.119 |
0.071 |
0.043 |
1.092 |
| Metro |
8 |
0.170 |
0.060 |
0.018 |
6.283 |
| Metro |
15 |
0.610 |
0.076 |
0.059 |
8.991 |
| Metro |
30 |
0.148 |
0.067 |
0.013 |
6.254 |
| DEMetro_Z |
2 |
0.158 |
0.065 |
0.042 |
2.214 |
| DEMetro_Z |
3 |
0.492 |
0.067 |
0.033 |
12.888 |
| DEMetro_Z |
5 |
1.330 |
0.071 |
0.043 |
29.093 |
| DEMetro_Z |
8 |
0.947 |
0.060 |
0.018 |
50.666 |
| DEMetro_Z |
15 |
3.645 |
0.076 |
0.059 |
60.080 |
| DEMetro_Z |
30 |
5.029 |
0.067 |
0.013 |
381.329 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.555 |
0.582 |
0.255 |
| HMC |
3 |
1.228 |
0.227 |
0.624 |
| HMC |
5 |
-1.843 |
0.0752 |
-0.340 |
| HMC |
8 |
-0.674 |
0.504 |
-0.142 |
| HMC |
15 |
-0.672 |
0.506 |
-0.131 |
| HMC |
30 |
1.006 |
0.322 |
1.067 |
| SMC |
2 |
-2.223 |
0.0333 |
-0.417 |
| SMC |
3 |
1.050 |
0.302 |
0.855 |
| SMC |
5 |
-0.994 |
0.327 |
-0.187 |
| SMC |
8 |
8.941 |
6.42e-12 |
3.005 |
| SMC |
15 |
1.065 |
0.295 |
0.196 |
| SMC |
30 |
47.861 |
1.37e-40 |
17.896 |
| Metro |
2 |
-0.394 |
0.695 |
-0.090 |
| Metro |
3 |
1.848 |
0.0725 |
0.936 |
| Metro |
5 |
-1.674 |
0.104 |
-0.310 |
| Metro |
8 |
0.671 |
0.506 |
0.267 |
| Metro |
15 |
0.676 |
0.504 |
0.418 |
| Metro |
30 |
1.594 |
0.121 |
1.733 |
| DEMetro_Z |
2 |
-0.983 |
0.331 |
-0.196 |
| DEMetro_Z |
3 |
1.624 |
0.115 |
8.572 |
| DEMetro_Z |
5 |
2.092 |
0.0452 |
4.185 |
| DEMetro_Z |
8 |
2.961 |
0.00582 |
2.905 |
| DEMetro_Z |
15 |
5.306 |
2.94e-06 |
1.895 |
| DEMetro_Z |
30 |
9.212 |
3.86e-10 |
29.666 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.575
|
0.126
|
0.288
|
| HMC_vs_SMC |
1
|
-0.302
|
0.765
|
-0.055
|
| HMC_vs_SMC |
2
|
-2.724
|
0.0108
|
-0.497
|
| HMC_vs_SMC |
3
|
-9.993
|
6.7e-11
|
-1.825
|
| HMC_vs_SMC |
4
|
-4.269
|
0.000192
|
-0.779
|
| HMC_vs_SMC |
5
|
-18.870
|
7.9e-18
|
-3.445
|
| Metro_vs_DEMetro_Z |
0
|
0.715
|
0.48
|
0.131
|
| Metro_vs_DEMetro_Z |
1
|
-1.430
|
0.163
|
-0.261
|
| Metro_vs_DEMetro_Z |
2
|
-2.251
|
0.0321
|
-0.411
|
| Metro_vs_DEMetro_Z |
3
|
-2.556
|
0.0161
|
-0.467
|
| Metro_vs_DEMetro_Z |
4
|
-2.241
|
0.0328
|
-0.409
|
| Metro_vs_DEMetro_Z |
5
|
-8.052
|
7.03e-09
|
-1.470
|
| HMC_vs_Metro |
0
|
0.786
|
0.438
|
0.144
|
| HMC_vs_Metro |
1
|
-0.819
|
0.419
|
-0.150
|
| HMC_vs_Metro |
2
|
-0.718
|
0.478
|
-0.131
|
| HMC_vs_Metro |
3
|
-1.147
|
0.261
|
-0.209
|
| HMC_vs_Metro |
4
|
-0.919
|
0.366
|
-0.168
|
| HMC_vs_Metro |
5
|
-2.030
|
0.0516
|
-0.371
|
| HMC_vs_DEMetro_Z |
0
|
1.029
|
0.312
|
0.188
|
| HMC_vs_DEMetro_Z |
1
|
-1.491
|
0.147
|
-0.272
|
| HMC_vs_DEMetro_Z |
2
|
-2.276
|
0.0304
|
-0.416
|
| HMC_vs_DEMetro_Z |
3
|
-3.183
|
0.00346
|
-0.581
|
| HMC_vs_DEMetro_Z |
4
|
-6.419
|
5.08e-07
|
-1.172
|
| HMC_vs_DEMetro_Z |
5
|
-8.379
|
3.1e-09
|
-1.530
|
| Metro_vs_SMC |
0
|
2.456
|
0.0203
|
0.448
|
| Metro_vs_SMC |
1
|
0.103
|
0.918
|
0.019
|
| Metro_vs_SMC |
2
|
-2.212
|
0.035
|
-0.404
|
| Metro_vs_SMC |
3
|
-5.234
|
1.32e-05
|
-0.956
|
| Metro_vs_SMC |
4
|
0.370
|
0.714
|
0.068
|
| Metro_vs_SMC |
5
|
-16.859
|
1.59e-16
|
-3.078
|
| DEMetro_Z_vs_SMC |
0
|
3.528
|
0.00141
|
0.644
|
| DEMetro_Z_vs_SMC |
1
|
1.435
|
0.162
|
0.262
|
| DEMetro_Z_vs_SMC |
2
|
2.192
|
0.0366
|
0.400
|
| DEMetro_Z_vs_SMC |
3
|
-0.099
|
0.922
|
-0.018
|
| DEMetro_Z_vs_SMC |
4
|
5.432
|
7.65e-06
|
0.992
|
| DEMetro_Z_vs_SMC |
5
|
3.743
|
0.0008
|
0.683
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
12.744 |
9.112 |
14.240 |
0.255 |
| HMC |
3 |
6.161 |
4.160 |
3.204 |
0.624 |
| HMC |
5 |
4.329 |
17.558 |
38.901 |
-0.340 |
| HMC |
8 |
4.226 |
5.290 |
7.509 |
-0.142 |
| HMC |
15 |
15.506 |
33.738 |
138.861 |
-0.131 |
| HMC |
30 |
11.344 |
5.218 |
5.743 |
1.067 |
| SMC |
2 |
3.173 |
9.112 |
14.240 |
-0.417 |
| SMC |
3 |
6.901 |
4.160 |
3.204 |
0.855 |
| SMC |
5 |
10.297 |
17.558 |
38.901 |
-0.187 |
| SMC |
8 |
27.856 |
5.290 |
7.509 |
3.005 |
| SMC |
15 |
60.985 |
33.738 |
138.861 |
0.196 |
| SMC |
30 |
108.004 |
5.218 |
5.743 |
17.896 |
| Metro |
2 |
7.833 |
9.112 |
14.240 |
-0.090 |
| Metro |
3 |
7.158 |
4.160 |
3.204 |
0.936 |
| Metro |
5 |
5.494 |
17.558 |
38.901 |
-0.310 |
| Metro |
8 |
7.293 |
5.290 |
7.509 |
0.267 |
| Metro |
15 |
91.748 |
33.738 |
138.861 |
0.418 |
| Metro |
30 |
15.170 |
5.218 |
5.743 |
1.733 |
| DEMetro_Z |
2 |
6.319 |
9.112 |
14.240 |
-0.196 |
| DEMetro_Z |
3 |
31.627 |
4.160 |
3.204 |
8.572 |
| DEMetro_Z |
5 |
180.374 |
17.558 |
38.901 |
4.185 |
| DEMetro_Z |
8 |
27.102 |
5.290 |
7.509 |
2.905 |
| DEMetro_Z |
15 |
296.877 |
33.738 |
138.861 |
1.895 |
| DEMetro_Z |
30 |
175.604 |
5.218 |
5.743 |
29.666 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.412 |
0.0214 |
1.565 |
| HMC |
3 |
3.038 |
0.00448 |
1.798 |
| HMC |
5 |
1.390 |
0.17 |
0.360 |
| HMC |
8 |
3.794 |
0.000584 |
2.481 |
| HMC |
15 |
2.792 |
0.00911 |
5.616 |
| HMC |
30 |
3.487 |
0.00157 |
16.864 |
| SMC |
2 |
-0.728 |
0.47 |
-0.179 |
| SMC |
3 |
4.804 |
4.01e-05 |
6.309 |
| SMC |
5 |
13.634 |
2.6e-14 |
23.198 |
| SMC |
8 |
19.998 |
1.56e-18 |
113.357 |
| SMC |
15 |
29.271 |
3.27e-23 |
83.791 |
| SMC |
30 |
123.490 |
2.84e-41 |
369.493 |
| Metro |
2 |
3.675 |
0.000901 |
3.894 |
| Metro |
3 |
6.543 |
2.65e-07 |
6.545 |
| Metro |
5 |
6.238 |
2.65e-07 |
3.055 |
| Metro |
8 |
3.681 |
0.000932 |
8.986 |
| Metro |
15 |
1.518 |
0.14 |
18.655 |
| Metro |
30 |
4.794 |
4.47e-05 |
22.312 |
| DEMetro_Z |
2 |
6.184 |
5.52e-07 |
4.365 |
| DEMetro_Z |
3 |
3.550 |
0.00134 |
44.381 |
| DEMetro_Z |
5 |
4.027 |
0.000372 |
73.721 |
| DEMetro_Z |
8 |
6.683 |
2.49e-07 |
94.597 |
| DEMetro_Z |
15 |
12.959 |
1.36e-13 |
196.007 |
| DEMetro_Z |
30 |
19.411 |
3.67e-18 |
485.364 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.362
|
0.72
|
-0.066
|
| Metro_vs_DEMetro_Z |
1
|
-2.961
|
0.00606
|
-0.541
|
| Metro_vs_DEMetro_Z |
2
|
-3.846
|
0.000607
|
-0.702
|
| Metro_vs_DEMetro_Z |
3
|
-5.994
|
1.62e-06
|
-1.094
|
| Metro_vs_DEMetro_Z |
4
|
-9.203
|
4.2e-10
|
-1.680
|
| Metro_vs_DEMetro_Z |
5
|
-18.388
|
1.58e-17
|
-3.357
|
| DEMetro_Z_vs_SMC |
0
|
6.635
|
2.83e-07
|
1.211
|
| DEMetro_Z_vs_SMC |
1
|
2.989
|
0.00566
|
0.546
|
| DEMetro_Z_vs_SMC |
2
|
2.743
|
0.0103
|
0.501
|
| DEMetro_Z_vs_SMC |
3
|
-1.300
|
0.204
|
-0.237
|
| DEMetro_Z_vs_SMC |
4
|
6.882
|
1.46e-07
|
1.257
|
| DEMetro_Z_vs_SMC |
5
|
4.743
|
5.18e-05
|
0.866
|
| HMC_vs_DEMetro_Z |
0
|
-3.348
|
0.00227
|
-0.611
|
| HMC_vs_DEMetro_Z |
1
|
-3.368
|
0.00215
|
-0.615
|
| HMC_vs_DEMetro_Z |
2
|
-4.005
|
0.000395
|
-0.731
|
| HMC_vs_DEMetro_Z |
3
|
-6.465
|
4.48e-07
|
-1.180
|
| HMC_vs_DEMetro_Z |
4
|
-12.346
|
4.53e-13
|
-2.254
|
| HMC_vs_DEMetro_Z |
5
|
-18.106
|
2.39e-17
|
-3.306
|
| HMC_vs_Metro |
0
|
-1.967
|
0.0588
|
-0.359
|
| HMC_vs_Metro |
1
|
-4.799
|
4.43e-05
|
-0.876
|
| HMC_vs_Metro |
2
|
-5.201
|
1.45e-05
|
-0.950
|
| HMC_vs_Metro |
3
|
-2.504
|
0.0182
|
-0.457
|
| HMC_vs_Metro |
4
|
-1.033
|
0.31
|
-0.189
|
| HMC_vs_Metro |
5
|
-0.862
|
0.396
|
-0.157
|
| HMC_vs_SMC |
0
|
2.813
|
0.00871
|
0.514
|
| HMC_vs_SMC |
1
|
-3.088
|
0.00441
|
-0.564
|
| HMC_vs_SMC |
2
|
-12.788
|
1.9e-13
|
-2.335
|
| HMC_vs_SMC |
3
|
-19.765
|
2.26e-18
|
-3.609
|
| HMC_vs_SMC |
4
|
-24.259
|
8.27e-21
|
-4.429
|
| HMC_vs_SMC |
5
|
-60.676
|
4.14e-32
|
-11.078
|
| Metro_vs_SMC |
0
|
3.889
|
0.000541
|
0.710
|
| Metro_vs_SMC |
1
|
0.144
|
0.887
|
0.026
|
| Metro_vs_SMC |
2
|
-11.213
|
4.62e-12
|
-2.047
|
| Metro_vs_SMC |
3
|
-15.527
|
1.37e-15
|
-2.835
|
| Metro_vs_SMC |
4
|
-4.862
|
3.72e-05
|
-0.888
|
| Metro_vs_SMC |
5
|
-60.744
|
4e-32
|
-11.090
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.179 |
0.124 |
0.035 |
1.565 |
| HMC |
3 |
0.146 |
0.115 |
0.018 |
1.798 |
| HMC |
5 |
0.140 |
0.126 |
0.039 |
0.360 |
| HMC |
8 |
0.166 |
0.113 |
0.021 |
2.481 |
| HMC |
15 |
0.440 |
0.136 |
0.054 |
5.616 |
| HMC |
30 |
0.429 |
0.118 |
0.018 |
16.864 |
| SMC |
2 |
0.118 |
0.124 |
0.035 |
-0.179 |
| SMC |
3 |
0.225 |
0.115 |
0.018 |
6.309 |
| SMC |
5 |
1.030 |
0.126 |
0.039 |
23.198 |
| SMC |
8 |
2.500 |
0.113 |
0.021 |
113.357 |
| SMC |
15 |
4.681 |
0.136 |
0.054 |
83.791 |
| SMC |
30 |
6.939 |
0.118 |
0.018 |
369.493 |
| Metro |
2 |
0.260 |
0.124 |
0.035 |
3.894 |
| Metro |
3 |
0.230 |
0.115 |
0.018 |
6.545 |
| Metro |
5 |
0.245 |
0.126 |
0.039 |
3.055 |
| Metro |
8 |
0.303 |
0.113 |
0.021 |
8.986 |
| Metro |
15 |
1.148 |
0.136 |
0.054 |
18.655 |
| Metro |
30 |
0.530 |
0.118 |
0.018 |
22.312 |
| DEMetro_Z |
2 |
0.276 |
0.124 |
0.035 |
4.365 |
| DEMetro_Z |
3 |
0.894 |
0.115 |
0.018 |
44.381 |
| DEMetro_Z |
5 |
2.998 |
0.126 |
0.039 |
73.721 |
| DEMetro_Z |
8 |
2.105 |
0.113 |
0.021 |
94.597 |
| DEMetro_Z |
15 |
10.769 |
0.136 |
0.054 |
196.007 |
| DEMetro_Z |
30 |
9.078 |
0.118 |
0.018 |
485.364 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.890 |
0.0059 |
1.089 |
| HMC |
3 |
3.448 |
0.00128 |
1.404 |
| HMC |
5 |
4.360 |
9.82e-05 |
2.218 |
| HMC |
8 |
2.632 |
0.0134 |
5.533 |
| HMC |
15 |
2.581 |
0.0152 |
34.188 |
| HMC |
30 |
2.754 |
0.01 |
47.294 |
| SMC |
2 |
0.849 |
0.4 |
0.221 |
| SMC |
3 |
7.061 |
7.26e-08 |
9.064 |
| SMC |
5 |
23.412 |
1.92e-20 |
88.696 |
| SMC |
8 |
31.555 |
4.66e-24 |
140.193 |
| SMC |
15 |
75.900 |
3.34e-35 |
190.517 |
| SMC |
30 |
148.111 |
7.8e-45 |
186.557 |
| Metro |
2 |
8.118 |
1.16e-09 |
4.454 |
| Metro |
3 |
8.550 |
6.18e-10 |
5.796 |
| Metro |
5 |
10.958 |
4.39e-12 |
12.970 |
| Metro |
8 |
8.608 |
1.34e-09 |
12.191 |
| Metro |
15 |
8.169 |
5.13e-09 |
40.552 |
| Metro |
30 |
8.830 |
9.95e-10 |
38.157 |
| DEMetro_Z |
2 |
9.015 |
4.19e-11 |
4.190 |
| DEMetro_Z |
3 |
6.327 |
6.37e-07 |
21.848 |
| DEMetro_Z |
5 |
8.741 |
1.27e-09 |
96.839 |
| DEMetro_Z |
8 |
15.140 |
2.6e-15 |
132.368 |
| DEMetro_Z |
15 |
35.345 |
2.02e-25 |
242.889 |
| DEMetro_Z |
30 |
65.404 |
3.64e-33 |
248.741 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
8.643
|
1.62e-09
|
1.578
|
| DEMetro_Z_vs_SMC |
1
|
3.215
|
0.00319
|
0.587
|
| DEMetro_Z_vs_SMC |
2
|
0.695
|
0.493
|
0.127
|
| DEMetro_Z_vs_SMC |
3
|
-0.856
|
0.399
|
-0.156
|
| DEMetro_Z_vs_SMC |
4
|
7.363
|
4.12e-08
|
1.344
|
| DEMetro_Z_vs_SMC |
5
|
14.552
|
7.33e-15
|
2.657
|
| HMC_vs_Metro |
0
|
-5.628
|
4.44e-06
|
-1.028
|
| HMC_vs_Metro |
1
|
-6.324
|
6.57e-07
|
-1.155
|
| HMC_vs_Metro |
2
|
-8.092
|
6.36e-09
|
-1.477
|
| HMC_vs_Metro |
3
|
-2.643
|
0.0131
|
-0.482
|
| HMC_vs_Metro |
4
|
-0.437
|
0.665
|
-0.080
|
| HMC_vs_Metro |
5
|
0.519
|
0.608
|
0.095
|
| Metro_vs_DEMetro_Z |
0
|
0.356
|
0.725
|
0.065
|
| Metro_vs_DEMetro_Z |
1
|
-4.459
|
0.000114
|
-0.814
|
| Metro_vs_DEMetro_Z |
2
|
-7.665
|
1.88e-08
|
-1.399
|
| Metro_vs_DEMetro_Z |
3
|
-14.110
|
1.61e-14
|
-2.576
|
| Metro_vs_DEMetro_Z |
4
|
-23.461
|
2.08e-20
|
-4.283
|
| Metro_vs_DEMetro_Z |
5
|
-38.651
|
1.69e-26
|
-7.057
|
| HMC_vs_SMC |
0
|
2.412
|
0.0224
|
0.440
|
| HMC_vs_SMC |
1
|
-5.863
|
2.32e-06
|
-1.070
|
| HMC_vs_SMC |
2
|
-21.712
|
1.75e-19
|
-3.964
|
| HMC_vs_SMC |
3
|
-28.905
|
6.25e-23
|
-5.277
|
| HMC_vs_SMC |
4
|
-12.179
|
6.32e-13
|
-2.223
|
| HMC_vs_SMC |
5
|
-8.210
|
4.72e-09
|
-1.499
|
| Metro_vs_SMC |
0
|
8.238
|
4.4e-09
|
1.504
|
| Metro_vs_SMC |
1
|
-2.349
|
0.0258
|
-0.429
|
| Metro_vs_SMC |
2
|
-19.143
|
5.36e-18
|
-3.495
|
| Metro_vs_SMC |
3
|
-28.520
|
9.1e-23
|
-5.207
|
| Metro_vs_SMC |
4
|
-25.099
|
3.22e-21
|
-4.582
|
| Metro_vs_SMC |
5
|
-31.883
|
3.96e-24
|
-5.821
|
| HMC_vs_DEMetro_Z |
0
|
-6.732
|
2.19e-07
|
-1.229
|
| HMC_vs_DEMetro_Z |
1
|
-5.771
|
2.99e-06
|
-1.054
|
| HMC_vs_DEMetro_Z |
2
|
-8.423
|
2.78e-09
|
-1.538
|
| HMC_vs_DEMetro_Z |
3
|
-13.874
|
2.47e-14
|
-2.533
|
| HMC_vs_DEMetro_Z |
4
|
-14.434
|
9.02e-15
|
-2.635
|
| HMC_vs_DEMetro_Z |
5
|
-11.305
|
3.8e-12
|
-2.064
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.020 |
0.015 |
0.005 |
1.089 |
| HMC |
3 |
0.020 |
0.015 |
0.003 |
1.404 |
| HMC |
5 |
0.019 |
0.014 |
0.002 |
2.218 |
| HMC |
8 |
0.027 |
0.015 |
0.002 |
5.533 |
| HMC |
15 |
0.084 |
0.015 |
0.002 |
34.188 |
| HMC |
30 |
0.115 |
0.016 |
0.002 |
47.294 |
| SMC |
2 |
0.016 |
0.015 |
0.005 |
0.221 |
| SMC |
3 |
0.047 |
0.015 |
0.003 |
9.064 |
| SMC |
5 |
0.211 |
0.014 |
0.002 |
88.696 |
| SMC |
8 |
0.332 |
0.015 |
0.002 |
140.193 |
| SMC |
15 |
0.400 |
0.015 |
0.002 |
190.517 |
| SMC |
30 |
0.407 |
0.016 |
0.002 |
186.557 |
| Metro |
2 |
0.035 |
0.015 |
0.005 |
4.454 |
| Metro |
3 |
0.035 |
0.015 |
0.003 |
5.796 |
| Metro |
5 |
0.043 |
0.014 |
0.002 |
12.970 |
| Metro |
8 |
0.043 |
0.015 |
0.002 |
12.191 |
| Metro |
15 |
0.097 |
0.015 |
0.002 |
40.552 |
| Metro |
30 |
0.096 |
0.016 |
0.002 |
38.157 |
| DEMetro_Z |
2 |
0.034 |
0.015 |
0.005 |
4.190 |
| DEMetro_Z |
3 |
0.091 |
0.015 |
0.003 |
21.848 |
| DEMetro_Z |
5 |
0.229 |
0.014 |
0.002 |
96.839 |
| DEMetro_Z |
8 |
0.314 |
0.015 |
0.002 |
132.368 |
| DEMetro_Z |
15 |
0.506 |
0.015 |
0.002 |
242.889 |
| DEMetro_Z |
30 |
0.537 |
0.016 |
0.002 |
248.741 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_high_Multimodality
(Mixture,
dimension,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.931 |
1.87e-06 |
17.932 |
| HMC |
3 |
6.787 |
1.83e-07 |
23.505 |
| HMC |
5 |
6.380 |
5.47e-07 |
20.254 |
| HMC |
8 |
6.620 |
2.91e-07 |
30.390 |
| HMC |
15 |
7.114 |
7.75e-08 |
30.750 |
| HMC |
30 |
6.543 |
3.61e-07 |
44.752 |
| SMC |
2 |
0.114 |
0.91 |
0.027 |
| SMC |
3 |
-0.407 |
0.686 |
-0.103 |
| SMC |
5 |
-0.877 |
0.384 |
-0.211 |
| SMC |
8 |
0.077 |
0.939 |
0.020 |
| SMC |
15 |
-0.239 |
0.812 |
-0.061 |
| SMC |
30 |
0.410 |
0.683 |
0.118 |
| Metro |
2 |
6.883 |
1.3e-07 |
12.289 |
| Metro |
3 |
5.919 |
1.82e-06 |
9.959 |
| Metro |
5 |
7.011 |
8.97e-08 |
11.117 |
| Metro |
8 |
5.452 |
7.04e-06 |
15.473 |
| Metro |
15 |
5.589 |
4.78e-06 |
14.662 |
| Metro |
30 |
6.856 |
1.5e-07 |
18.475 |
| DEMetro_Z |
2 |
7.455 |
2.79e-08 |
12.470 |
| DEMetro_Z |
3 |
7.582 |
2.23e-08 |
23.627 |
| DEMetro_Z |
5 |
15.632 |
1.12e-15 |
101.051 |
| DEMetro_Z |
8 |
19.561 |
2.97e-18 |
309.818 |
| DEMetro_Z |
15 |
31.532 |
5.35e-24 |
515.846 |
| DEMetro_Z |
30 |
43.506 |
5.75e-28 |
1186.177 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
1.633
|
0.113
|
0.298
|
| HMC_vs_DEMetro_Z |
1
|
-0.024
|
0.981
|
-0.004
|
| HMC_vs_DEMetro_Z |
2
|
-10.873
|
9.55e-12
|
-1.985
|
| HMC_vs_DEMetro_Z |
3
|
-16.098
|
5.36e-16
|
-2.939
|
| HMC_vs_DEMetro_Z |
4
|
-30.305
|
1.65e-23
|
-5.533
|
| HMC_vs_DEMetro_Z |
5
|
-40.525
|
4.38e-27
|
-7.399
|
| Metro_vs_SMC |
0
|
6.862
|
1.54e-07
|
1.253
|
| Metro_vs_SMC |
1
|
5.988
|
1.65e-06
|
1.093
|
| Metro_vs_SMC |
2
|
7.161
|
7e-08
|
1.307
|
| Metro_vs_SMC |
3
|
5.559
|
5.37e-06
|
1.015
|
| Metro_vs_SMC |
4
|
5.719
|
3.45e-06
|
1.044
|
| Metro_vs_SMC |
5
|
6.923
|
1.31e-07
|
1.264
|
| Metro_vs_DEMetro_Z |
0
|
-0.065
|
0.948
|
-0.012
|
| Metro_vs_DEMetro_Z |
1
|
-3.810
|
0.000669
|
-0.696
|
| Metro_vs_DEMetro_Z |
2
|
-13.040
|
1.17e-13
|
-2.381
|
| Metro_vs_DEMetro_Z |
3
|
-17.744
|
4.09e-17
|
-3.240
|
| Metro_vs_DEMetro_Z |
4
|
-31.310
|
6.6e-24
|
-5.716
|
| Metro_vs_DEMetro_Z |
5
|
-41.574
|
2.11e-27
|
-7.590
|
| HMC_vs_Metro |
0
|
1.637
|
0.112
|
0.299
|
| HMC_vs_Metro |
1
|
3.784
|
0.000718
|
0.691
|
| HMC_vs_Metro |
2
|
3.023
|
0.0052
|
0.552
|
| HMC_vs_Metro |
3
|
2.890
|
0.00722
|
0.528
|
| HMC_vs_Metro |
4
|
3.591
|
0.0012
|
0.656
|
| HMC_vs_Metro |
5
|
3.493
|
0.00155
|
0.638
|
| HMC_vs_SMC |
0
|
5.928
|
1.94e-06
|
1.082
|
| HMC_vs_SMC |
1
|
6.816
|
1.75e-07
|
1.244
|
| HMC_vs_SMC |
2
|
6.433
|
4.89e-07
|
1.175
|
| HMC_vs_SMC |
3
|
6.574
|
3.34e-07
|
1.200
|
| HMC_vs_SMC |
4
|
7.132
|
7.55e-08
|
1.302
|
| HMC_vs_SMC |
5
|
6.566
|
3.41e-07
|
1.199
|
| DEMetro_Z_vs_SMC |
0
|
7.536
|
2.63e-08
|
1.376
|
| DEMetro_Z_vs_SMC |
1
|
7.526
|
2.69e-08
|
1.374
|
| DEMetro_Z_vs_SMC |
2
|
15.628
|
1.16e-15
|
2.853
|
| DEMetro_Z_vs_SMC |
3
|
19.520
|
3.17e-18
|
3.564
|
| DEMetro_Z_vs_SMC |
4
|
31.578
|
5.18e-24
|
5.765
|
| DEMetro_Z_vs_SMC |
5
|
43.451
|
5.98e-28
|
7.933
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.774 |
0.058 |
0.040 |
17.932 |
| HMC |
3 |
0.835 |
0.052 |
0.033 |
23.505 |
| HMC |
5 |
0.548 |
0.041 |
0.025 |
20.254 |
| HMC |
8 |
0.507 |
0.035 |
0.016 |
30.390 |
| HMC |
15 |
0.388 |
0.032 |
0.012 |
30.750 |
| HMC |
30 |
0.286 |
0.028 |
0.006 |
44.752 |
| SMC |
2 |
0.059 |
0.058 |
0.040 |
0.027 |
| SMC |
3 |
0.049 |
0.052 |
0.033 |
-0.103 |
| SMC |
5 |
0.036 |
0.041 |
0.025 |
-0.211 |
| SMC |
8 |
0.036 |
0.035 |
0.016 |
0.020 |
| SMC |
15 |
0.031 |
0.032 |
0.012 |
-0.061 |
| SMC |
30 |
0.028 |
0.028 |
0.006 |
0.118 |
| Metro |
2 |
0.549 |
0.058 |
0.040 |
12.289 |
| Metro |
3 |
0.384 |
0.052 |
0.033 |
9.959 |
| Metro |
5 |
0.319 |
0.041 |
0.025 |
11.117 |
| Metro |
8 |
0.276 |
0.035 |
0.016 |
15.473 |
| Metro |
15 |
0.202 |
0.032 |
0.012 |
14.662 |
| Metro |
30 |
0.134 |
0.028 |
0.006 |
18.475 |
| DEMetro_Z |
2 |
0.556 |
0.058 |
0.040 |
12.470 |
| DEMetro_Z |
3 |
0.839 |
0.052 |
0.033 |
23.627 |
| DEMetro_Z |
5 |
2.568 |
0.041 |
0.025 |
101.051 |
| DEMetro_Z |
8 |
4.846 |
0.035 |
0.016 |
309.818 |
| DEMetro_Z |
15 |
6.012 |
0.032 |
0.012 |
515.846 |
| DEMetro_Z |
30 |
6.865 |
0.028 |
0.006 |
1186.177 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.475 |
0.00162 |
18.712 |
| HMC |
3 |
4.137 |
0.000275 |
39.514 |
| HMC |
5 |
3.908 |
0.000512 |
29.043 |
| HMC |
8 |
4.339 |
0.000157 |
22.068 |
| HMC |
15 |
4.309 |
0.000171 |
22.348 |
| HMC |
30 |
4.278 |
0.000187 |
62.215 |
| SMC |
2 |
2.139 |
0.0369 |
0.648 |
| SMC |
3 |
0.963 |
0.339 |
0.269 |
| SMC |
5 |
0.507 |
0.615 |
0.194 |
| SMC |
8 |
-1.355 |
0.182 |
-0.293 |
| SMC |
15 |
-1.102 |
0.275 |
-0.254 |
| SMC |
30 |
3.984 |
0.000238 |
1.461 |
| Metro |
2 |
4.339 |
0.000152 |
7.459 |
| Metro |
3 |
4.206 |
0.000222 |
8.290 |
| Metro |
5 |
4.172 |
0.000245 |
9.253 |
| Metro |
8 |
3.428 |
0.00182 |
6.864 |
| Metro |
15 |
3.426 |
0.00181 |
5.645 |
| Metro |
30 |
5.507 |
5.9e-06 |
11.322 |
| DEMetro_Z |
2 |
4.285 |
0.000176 |
7.234 |
| DEMetro_Z |
3 |
5.271 |
1.19e-05 |
44.355 |
| DEMetro_Z |
5 |
9.933 |
7.68e-11 |
1234.192 |
| DEMetro_Z |
8 |
13.243 |
7.97e-14 |
1926.413 |
| DEMetro_Z |
15 |
21.902 |
1.38e-19 |
3800.701 |
| DEMetro_Z |
30 |
45.523 |
1.58e-28 |
14531.322 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.336
|
0.00234
|
0.609
|
| HMC_vs_SMC |
1
|
4.099
|
0.000306
|
0.748
|
| HMC_vs_SMC |
2
|
3.860
|
0.000584
|
0.705
|
| HMC_vs_SMC |
3
|
4.427
|
0.000124
|
0.808
|
| HMC_vs_SMC |
4
|
4.352
|
0.000153
|
0.795
|
| HMC_vs_SMC |
5
|
4.192
|
0.000237
|
0.765
|
| Metro_vs_DEMetro_Z |
0
|
0.082
|
0.935
|
0.015
|
| Metro_vs_DEMetro_Z |
1
|
-4.053
|
0.000347
|
-0.740
|
| Metro_vs_DEMetro_Z |
2
|
-9.858
|
9.13e-11
|
-1.800
|
| Metro_vs_DEMetro_Z |
3
|
-13.159
|
9.34e-14
|
-2.403
|
| Metro_vs_DEMetro_Z |
4
|
-21.858
|
1.46e-19
|
-3.991
|
| Metro_vs_DEMetro_Z |
5
|
-45.499
|
1.6e-28
|
-8.307
|
| HMC_vs_Metro |
0
|
2.008
|
0.054
|
0.367
|
| HMC_vs_Metro |
1
|
3.344
|
0.00229
|
0.611
|
| HMC_vs_Metro |
2
|
2.864
|
0.00771
|
0.523
|
| HMC_vs_Metro |
3
|
2.851
|
0.00795
|
0.521
|
| HMC_vs_Metro |
4
|
3.399
|
0.00199
|
0.620
|
| HMC_vs_Metro |
5
|
3.423
|
0.00187
|
0.625
|
| HMC_vs_DEMetro_Z |
0
|
2.039
|
0.0506
|
0.372
|
| HMC_vs_DEMetro_Z |
1
|
-0.357
|
0.724
|
-0.065
|
| HMC_vs_DEMetro_Z |
2
|
-9.621
|
1.57e-10
|
-1.757
|
| HMC_vs_DEMetro_Z |
3
|
-13.003
|
1.26e-13
|
-2.374
|
| HMC_vs_DEMetro_Z |
4
|
-21.678
|
1.83e-19
|
-3.958
|
| HMC_vs_DEMetro_Z |
5
|
-45.084
|
2.08e-28
|
-8.231
|
| Metro_vs_SMC |
0
|
4.060
|
0.00034
|
0.741
|
| Metro_vs_SMC |
1
|
3.992
|
0.000409
|
0.729
|
| Metro_vs_SMC |
2
|
3.996
|
0.000404
|
0.730
|
| Metro_vs_SMC |
3
|
3.534
|
0.00139
|
0.645
|
| Metro_vs_SMC |
4
|
3.594
|
0.00119
|
0.656
|
| Metro_vs_SMC |
5
|
4.599
|
7.71e-05
|
0.840
|
| DEMetro_Z_vs_SMC |
0
|
3.900
|
0.000524
|
0.712
|
| DEMetro_Z_vs_SMC |
1
|
5.195
|
1.48e-05
|
0.948
|
| DEMetro_Z_vs_SMC |
2
|
9.931
|
7.72e-11
|
1.813
|
| DEMetro_Z_vs_SMC |
3
|
13.248
|
7.9e-14
|
2.419
|
| DEMetro_Z_vs_SMC |
4
|
21.908
|
1.37e-19
|
4.000
|
| DEMetro_Z_vs_SMC |
5
|
45.530
|
1.57e-28
|
8.313
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
1.455 |
0.091 |
0.073 |
18.712 |
| HMC |
3 |
1.871 |
0.072 |
0.046 |
39.514 |
| HMC |
5 |
1.078 |
0.071 |
0.035 |
29.043 |
| HMC |
8 |
1.140 |
0.074 |
0.048 |
22.068 |
| HMC |
15 |
0.870 |
0.061 |
0.036 |
22.348 |
| HMC |
30 |
0.725 |
0.041 |
0.011 |
62.215 |
| SMC |
2 |
0.138 |
0.091 |
0.073 |
0.648 |
| SMC |
3 |
0.085 |
0.072 |
0.046 |
0.269 |
| SMC |
5 |
0.078 |
0.071 |
0.035 |
0.194 |
| SMC |
8 |
0.060 |
0.074 |
0.048 |
-0.293 |
| SMC |
15 |
0.052 |
0.061 |
0.036 |
-0.254 |
| SMC |
30 |
0.058 |
0.041 |
0.011 |
1.461 |
| Metro |
2 |
0.635 |
0.091 |
0.073 |
7.459 |
| Metro |
3 |
0.450 |
0.072 |
0.046 |
8.290 |
| Metro |
5 |
0.392 |
0.071 |
0.035 |
9.253 |
| Metro |
8 |
0.406 |
0.074 |
0.048 |
6.864 |
| Metro |
15 |
0.265 |
0.061 |
0.036 |
5.645 |
| Metro |
30 |
0.166 |
0.041 |
0.011 |
11.322 |
| DEMetro_Z |
2 |
0.618 |
0.091 |
0.073 |
7.234 |
| DEMetro_Z |
3 |
2.091 |
0.072 |
0.046 |
44.355 |
| DEMetro_Z |
5 |
42.868 |
0.071 |
0.035 |
1234.192 |
| DEMetro_Z |
8 |
93.082 |
0.074 |
0.048 |
1926.413 |
| DEMetro_Z |
15 |
137.656 |
0.061 |
0.036 |
3800.701 |
| DEMetro_Z |
30 |
159.635 |
0.041 |
0.011 |
14531.322 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.891 |
2.1e-06 |
20.456 |
| HMC |
3 |
6.727 |
2.16e-07 |
26.127 |
| HMC |
5 |
6.371 |
5.65e-07 |
22.993 |
| HMC |
8 |
6.670 |
2.56e-07 |
38.183 |
| HMC |
15 |
6.748 |
2.07e-07 |
40.921 |
| HMC |
30 |
6.316 |
6.7e-07 |
58.770 |
| SMC |
2 |
0.126 |
0.9 |
0.030 |
| SMC |
3 |
-0.052 |
0.959 |
-0.013 |
| SMC |
5 |
-0.930 |
0.357 |
-0.222 |
| SMC |
8 |
-0.385 |
0.702 |
-0.101 |
| SMC |
15 |
-0.289 |
0.773 |
-0.072 |
| SMC |
30 |
1.260 |
0.213 |
0.369 |
| Metro |
2 |
6.871 |
1.39e-07 |
14.381 |
| Metro |
3 |
5.882 |
2.06e-06 |
11.238 |
| Metro |
5 |
6.746 |
1.88e-07 |
11.634 |
| Metro |
8 |
5.507 |
6.09e-06 |
19.002 |
| Metro |
15 |
5.656 |
4.02e-06 |
18.754 |
| Metro |
30 |
6.931 |
1.25e-07 |
23.462 |
| DEMetro_Z |
2 |
7.567 |
2.17e-08 |
14.831 |
| DEMetro_Z |
3 |
7.764 |
1.4e-08 |
26.353 |
| DEMetro_Z |
5 |
16.134 |
5e-16 |
185.769 |
| DEMetro_Z |
8 |
22.290 |
8.52e-20 |
688.574 |
| DEMetro_Z |
15 |
40.598 |
4.15e-27 |
1264.014 |
| DEMetro_Z |
30 |
87.713 |
9.96e-37 |
2878.778 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.137
|
0.892
|
-0.025
|
| Metro_vs_DEMetro_Z |
1
|
-3.820
|
0.00065
|
-0.697
|
| Metro_vs_DEMetro_Z |
2
|
-14.969
|
3.54e-15
|
-2.733
|
| Metro_vs_DEMetro_Z |
3
|
-20.927
|
4.79e-19
|
-3.821
|
| Metro_vs_DEMetro_Z |
4
|
-40.001
|
6.34e-27
|
-7.303
|
| Metro_vs_DEMetro_Z |
5
|
-84.423
|
3.02e-36
|
-15.414
|
| DEMetro_Z_vs_SMC |
0
|
7.634
|
2.04e-08
|
1.394
|
| DEMetro_Z_vs_SMC |
1
|
7.677
|
1.83e-08
|
1.402
|
| DEMetro_Z_vs_SMC |
2
|
16.116
|
5.2e-16
|
2.942
|
| DEMetro_Z_vs_SMC |
3
|
22.278
|
8.65e-20
|
4.067
|
| DEMetro_Z_vs_SMC |
4
|
40.625
|
4.08e-27
|
7.417
|
| DEMetro_Z_vs_SMC |
5
|
87.777
|
9.79e-37
|
16.026
|
| HMC_vs_DEMetro_Z |
0
|
1.483
|
0.149
|
0.271
|
| HMC_vs_DEMetro_Z |
1
|
-0.039
|
0.969
|
-0.007
|
| HMC_vs_DEMetro_Z |
2
|
-13.275
|
7.5e-14
|
-2.424
|
| HMC_vs_DEMetro_Z |
3
|
-19.624
|
2.75e-18
|
-3.583
|
| HMC_vs_DEMetro_Z |
4
|
-37.962
|
2.81e-26
|
-6.931
|
| HMC_vs_DEMetro_Z |
5
|
-84.529
|
2.91e-36
|
-15.433
|
| HMC_vs_Metro |
0
|
1.532
|
0.136
|
0.280
|
| HMC_vs_Metro |
1
|
3.677
|
0.000954
|
0.671
|
| HMC_vs_Metro |
2
|
3.259
|
0.00286
|
0.595
|
| HMC_vs_Metro |
3
|
2.999
|
0.00551
|
0.548
|
| HMC_vs_Metro |
4
|
3.640
|
0.00105
|
0.665
|
| HMC_vs_Metro |
5
|
3.479
|
0.00161
|
0.635
|
| HMC_vs_SMC |
0
|
5.872
|
2.27e-06
|
1.072
|
| HMC_vs_SMC |
1
|
6.741
|
2.13e-07
|
1.231
|
| HMC_vs_SMC |
2
|
6.425
|
4.99e-07
|
1.173
|
| HMC_vs_SMC |
3
|
6.656
|
2.68e-07
|
1.215
|
| HMC_vs_SMC |
4
|
6.766
|
2e-07
|
1.235
|
| HMC_vs_SMC |
5
|
6.308
|
6.87e-07
|
1.152
|
| Metro_vs_SMC |
0
|
6.870
|
1.51e-07
|
1.254
|
| Metro_vs_SMC |
1
|
5.884
|
2.19e-06
|
1.074
|
| Metro_vs_SMC |
2
|
6.885
|
1.45e-07
|
1.257
|
| Metro_vs_SMC |
3
|
5.632
|
4.38e-06
|
1.028
|
| Metro_vs_SMC |
4
|
5.758
|
3.1e-06
|
1.051
|
| Metro_vs_SMC |
5
|
6.884
|
1.46e-07
|
1.257
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.686 |
0.069 |
0.030 |
20.456 |
| HMC |
3 |
0.723 |
0.059 |
0.025 |
26.127 |
| HMC |
5 |
0.482 |
0.050 |
0.019 |
22.993 |
| HMC |
8 |
0.429 |
0.043 |
0.010 |
38.183 |
| HMC |
15 |
0.324 |
0.038 |
0.007 |
40.921 |
| HMC |
30 |
0.236 |
0.034 |
0.003 |
58.770 |
| SMC |
2 |
0.070 |
0.069 |
0.030 |
0.030 |
| SMC |
3 |
0.059 |
0.059 |
0.025 |
-0.013 |
| SMC |
5 |
0.045 |
0.050 |
0.019 |
-0.222 |
| SMC |
8 |
0.042 |
0.043 |
0.010 |
-0.101 |
| SMC |
15 |
0.038 |
0.038 |
0.007 |
-0.072 |
| SMC |
30 |
0.035 |
0.034 |
0.003 |
0.369 |
| Metro |
2 |
0.502 |
0.069 |
0.030 |
14.381 |
| Metro |
3 |
0.345 |
0.059 |
0.025 |
11.238 |
| Metro |
5 |
0.268 |
0.050 |
0.019 |
11.634 |
| Metro |
8 |
0.235 |
0.043 |
0.010 |
19.002 |
| Metro |
15 |
0.169 |
0.038 |
0.007 |
18.754 |
| Metro |
30 |
0.115 |
0.034 |
0.003 |
23.462 |
| DEMetro_Z |
2 |
0.516 |
0.069 |
0.030 |
14.831 |
| DEMetro_Z |
3 |
0.729 |
0.059 |
0.025 |
26.353 |
| DEMetro_Z |
5 |
3.543 |
0.050 |
0.019 |
185.769 |
| DEMetro_Z |
8 |
7.007 |
0.043 |
0.010 |
688.574 |
| DEMetro_Z |
15 |
8.877 |
0.038 |
0.007 |
1264.014 |
| DEMetro_Z |
30 |
9.945 |
0.034 |
0.003 |
2878.778 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.829 |
2.51e-06 |
22.728 |
| HMC |
3 |
6.705 |
2.3e-07 |
25.979 |
| HMC |
5 |
6.208 |
8.83e-07 |
22.790 |
| HMC |
8 |
6.548 |
3.55e-07 |
36.099 |
| HMC |
15 |
6.846 |
1.59e-07 |
35.716 |
| HMC |
30 |
6.566 |
3.39e-07 |
50.157 |
| SMC |
2 |
0.694 |
0.491 |
0.172 |
| SMC |
3 |
-0.203 |
0.84 |
-0.048 |
| SMC |
5 |
-1.037 |
0.304 |
-0.251 |
| SMC |
8 |
-0.179 |
0.859 |
-0.048 |
| SMC |
15 |
-0.304 |
0.762 |
-0.078 |
| SMC |
30 |
1.376 |
0.174 |
0.416 |
| Metro |
2 |
6.835 |
1.55e-07 |
15.284 |
| Metro |
3 |
5.977 |
1.57e-06 |
10.814 |
| Metro |
5 |
6.764 |
1.82e-07 |
12.563 |
| Metro |
8 |
5.357 |
9.25e-06 |
18.086 |
| Metro |
15 |
5.443 |
7.25e-06 |
16.885 |
| Metro |
30 |
6.943 |
1.2e-07 |
21.285 |
| DEMetro_Z |
2 |
7.311 |
4.33e-08 |
15.866 |
| DEMetro_Z |
3 |
7.169 |
6.62e-08 |
24.396 |
| DEMetro_Z |
5 |
29.557 |
2.12e-23 |
68.333 |
| DEMetro_Z |
8 |
70.922 |
1.28e-34 |
126.627 |
| DEMetro_Z |
15 |
71.524 |
1.28e-34 |
142.123 |
| DEMetro_Z |
30 |
122.029 |
2.05e-41 |
247.740 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.318
|
4.63e-08
|
1.336
|
| DEMetro_Z_vs_SMC |
1
|
7.118
|
7.84e-08
|
1.300
|
| DEMetro_Z_vs_SMC |
2
|
29.219
|
4.61e-23
|
5.335
|
| DEMetro_Z_vs_SMC |
3
|
70.238
|
6.1e-34
|
12.824
|
| DEMetro_Z_vs_SMC |
4
|
72.514
|
2.43e-34
|
13.239
|
| DEMetro_Z_vs_SMC |
5
|
121.028
|
9.04e-41
|
22.097
|
| HMC_vs_Metro |
0
|
1.690
|
0.102
|
0.309
|
| HMC_vs_Metro |
1
|
3.794
|
0.000697
|
0.693
|
| HMC_vs_Metro |
2
|
2.895
|
0.00714
|
0.528
|
| HMC_vs_Metro |
3
|
2.913
|
0.00682
|
0.532
|
| HMC_vs_Metro |
4
|
3.506
|
0.0015
|
0.640
|
| HMC_vs_Metro |
5
|
3.464
|
0.00168
|
0.632
|
| Metro_vs_DEMetro_Z |
0
|
-0.166
|
0.87
|
-0.030
|
| Metro_vs_DEMetro_Z |
1
|
-3.530
|
0.00141
|
-0.644
|
| Metro_vs_DEMetro_Z |
2
|
-19.696
|
2.49e-18
|
-3.596
|
| Metro_vs_DEMetro_Z |
3
|
-28.460
|
9.65e-23
|
-5.196
|
| Metro_vs_DEMetro_Z |
4
|
-46.017
|
1.16e-28
|
-8.402
|
| Metro_vs_DEMetro_Z |
5
|
-62.283
|
1.95e-32
|
-11.371
|
| HMC_vs_SMC |
0
|
5.789
|
2.84e-06
|
1.057
|
| HMC_vs_SMC |
1
|
6.713
|
2.3e-07
|
1.226
|
| HMC_vs_SMC |
2
|
6.265
|
7.72e-07
|
1.144
|
| HMC_vs_SMC |
3
|
6.514
|
3.93e-07
|
1.189
|
| HMC_vs_SMC |
4
|
6.876
|
1.49e-07
|
1.255
|
| HMC_vs_SMC |
5
|
6.560
|
3.47e-07
|
1.198
|
| Metro_vs_SMC |
0
|
6.800
|
1.82e-07
|
1.242
|
| Metro_vs_SMC |
1
|
6.015
|
1.53e-06
|
1.098
|
| Metro_vs_SMC |
2
|
6.906
|
1.37e-07
|
1.261
|
| Metro_vs_SMC |
3
|
5.459
|
7.09e-06
|
0.997
|
| Metro_vs_SMC |
4
|
5.556
|
5.41e-06
|
1.014
|
| Metro_vs_SMC |
5
|
6.881
|
1.47e-07
|
1.256
|
| HMC_vs_DEMetro_Z |
0
|
1.600
|
0.12
|
0.292
|
| HMC_vs_DEMetro_Z |
1
|
0.277
|
0.784
|
0.051
|
| HMC_vs_DEMetro_Z |
2
|
-10.539
|
1.98e-11
|
-1.924
|
| HMC_vs_DEMetro_Z |
3
|
-16.940
|
1.4e-16
|
-3.093
|
| HMC_vs_DEMetro_Z |
4
|
-20.642
|
6.96e-19
|
-3.769
|
| HMC_vs_DEMetro_Z |
5
|
-25.947
|
1.28e-21
|
-4.737
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.167 |
0.013 |
0.007 |
22.728 |
| HMC |
3 |
0.214 |
0.014 |
0.008 |
25.979 |
| HMC |
5 |
0.165 |
0.014 |
0.007 |
22.790 |
| HMC |
8 |
0.179 |
0.014 |
0.005 |
36.099 |
| HMC |
15 |
0.159 |
0.014 |
0.004 |
35.716 |
| HMC |
30 |
0.129 |
0.014 |
0.002 |
50.157 |
| SMC |
2 |
0.014 |
0.013 |
0.007 |
0.172 |
| SMC |
3 |
0.013 |
0.014 |
0.008 |
-0.048 |
| SMC |
5 |
0.012 |
0.014 |
0.007 |
-0.251 |
| SMC |
8 |
0.014 |
0.014 |
0.005 |
-0.048 |
| SMC |
15 |
0.014 |
0.014 |
0.004 |
-0.078 |
| SMC |
30 |
0.015 |
0.014 |
0.002 |
0.416 |
| Metro |
2 |
0.117 |
0.013 |
0.007 |
15.284 |
| Metro |
3 |
0.097 |
0.014 |
0.008 |
10.814 |
| Metro |
5 |
0.097 |
0.014 |
0.007 |
12.563 |
| Metro |
8 |
0.096 |
0.014 |
0.005 |
18.086 |
| Metro |
15 |
0.083 |
0.014 |
0.004 |
16.885 |
| Metro |
30 |
0.063 |
0.014 |
0.002 |
21.285 |
| DEMetro_Z |
2 |
0.121 |
0.013 |
0.007 |
15.866 |
| DEMetro_Z |
3 |
0.201 |
0.014 |
0.008 |
24.396 |
| DEMetro_Z |
5 |
0.468 |
0.014 |
0.007 |
68.333 |
| DEMetro_Z |
8 |
0.592 |
0.014 |
0.005 |
126.627 |
| DEMetro_Z |
15 |
0.589 |
0.014 |
0.004 |
142.123 |
| DEMetro_Z |
30 |
0.580 |
0.014 |
0.002 |
247.740 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
8.352 |
3.24e-09 |
40.878 |
| HMC |
3 |
7.828 |
1.22e-08 |
38.736 |
| HMC |
5 |
8.779 |
1.13e-09 |
41.988 |
| HMC |
8 |
9.981 |
6.76e-11 |
60.582 |
| HMC |
15 |
9.277 |
3.45e-10 |
52.155 |
| HMC |
30 |
8.644 |
1.6e-09 |
69.149 |
| SMC |
2 |
-0.642 |
0.524 |
-0.148 |
| SMC |
3 |
-1.487 |
0.143 |
-0.344 |
| SMC |
5 |
-1.023 |
0.311 |
-0.233 |
| SMC |
8 |
-0.828 |
0.411 |
-0.201 |
| SMC |
15 |
-0.847 |
0.401 |
-0.195 |
| SMC |
30 |
1.480 |
0.145 |
0.448 |
| Metro |
2 |
6.334 |
5.93e-07 |
12.532 |
| Metro |
3 |
5.979 |
1.55e-06 |
10.683 |
| Metro |
5 |
7.316 |
3.98e-08 |
11.656 |
| Metro |
8 |
6.907 |
1.26e-07 |
14.236 |
| Metro |
15 |
8.360 |
2.67e-09 |
13.637 |
| Metro |
30 |
5.716 |
3.4e-06 |
17.867 |
| DEMetro_Z |
2 |
4.272 |
0.000183 |
7.504 |
| DEMetro_Z |
3 |
6.176 |
9.7e-07 |
28.645 |
| DEMetro_Z |
5 |
10.722 |
1.3e-11 |
71.393 |
| DEMetro_Z |
8 |
11.365 |
3.35e-12 |
392.464 |
| DEMetro_Z |
15 |
18.228 |
2e-17 |
776.310 |
| DEMetro_Z |
30 |
32.418 |
2.47e-24 |
1934.906 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
6.545
|
3.61e-07
|
1.195
|
| HMC_vs_DEMetro_Z |
1
|
1.598
|
0.121
|
0.292
|
| HMC_vs_DEMetro_Z |
2
|
-3.650
|
0.00103
|
-0.666
|
| HMC_vs_DEMetro_Z |
3
|
-9.656
|
1.45e-10
|
-1.763
|
| HMC_vs_DEMetro_Z |
4
|
-16.754
|
1.88e-16
|
-3.059
|
| HMC_vs_DEMetro_Z |
5
|
-30.224
|
1.78e-23
|
-5.518
|
| Metro_vs_SMC |
0
|
6.294
|
7.13e-07
|
1.149
|
| Metro_vs_SMC |
1
|
6.117
|
1.16e-06
|
1.117
|
| Metro_vs_SMC |
2
|
7.340
|
4.37e-08
|
1.340
|
| Metro_vs_SMC |
3
|
6.990
|
1.1e-07
|
1.276
|
| Metro_vs_SMC |
4
|
8.649
|
1.6e-09
|
1.579
|
| Metro_vs_SMC |
5
|
5.508
|
6.19e-06
|
1.006
|
| Metro_vs_DEMetro_Z |
0
|
1.954
|
0.0604
|
0.357
|
| Metro_vs_DEMetro_Z |
1
|
-3.759
|
0.000766
|
-0.686
|
| Metro_vs_DEMetro_Z |
2
|
-9.041
|
6.18e-10
|
-1.651
|
| Metro_vs_DEMetro_Z |
3
|
-10.948
|
8.14e-12
|
-1.999
|
| Metro_vs_DEMetro_Z |
4
|
-18.224
|
2.01e-17
|
-3.327
|
| Metro_vs_DEMetro_Z |
5
|
-32.200
|
2.99e-24
|
-5.879
|
| HMC_vs_Metro |
0
|
5.180
|
1.54e-05
|
0.946
|
| HMC_vs_Metro |
1
|
5.044
|
2.24e-05
|
0.921
|
| HMC_vs_Metro |
2
|
5.690
|
3.74e-06
|
1.039
|
| HMC_vs_Metro |
3
|
6.704
|
2.35e-07
|
1.224
|
| HMC_vs_Metro |
4
|
6.327
|
6.52e-07
|
1.155
|
| HMC_vs_Metro |
5
|
5.605
|
4.72e-06
|
1.023
|
| HMC_vs_SMC |
0
|
8.341
|
3.4e-09
|
1.523
|
| HMC_vs_SMC |
1
|
7.928
|
9.63e-09
|
1.447
|
| HMC_vs_SMC |
2
|
8.858
|
9.59e-10
|
1.617
|
| HMC_vs_SMC |
3
|
9.985
|
6.82e-11
|
1.823
|
| HMC_vs_SMC |
4
|
9.179
|
4.44e-10
|
1.676
|
| HMC_vs_SMC |
5
|
8.626
|
1.69e-09
|
1.575
|
| DEMetro_Z_vs_SMC |
0
|
4.342
|
0.000157
|
0.793
|
| DEMetro_Z_vs_SMC |
1
|
6.238
|
8.3e-07
|
1.139
|
| DEMetro_Z_vs_SMC |
2
|
10.709
|
1.36e-11
|
1.955
|
| DEMetro_Z_vs_SMC |
3
|
11.382
|
3.24e-12
|
2.078
|
| DEMetro_Z_vs_SMC |
4
|
18.242
|
1.95e-17
|
3.331
|
| DEMetro_Z_vs_SMC |
5
|
32.415
|
2.48e-24
|
5.918
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
1.691 |
0.058 |
0.040 |
40.878 |
| HMC |
3 |
1.342 |
0.052 |
0.033 |
38.736 |
| HMC |
5 |
1.091 |
0.041 |
0.025 |
41.988 |
| HMC |
8 |
0.976 |
0.035 |
0.016 |
60.582 |
| HMC |
15 |
0.636 |
0.032 |
0.012 |
52.155 |
| HMC |
30 |
0.426 |
0.028 |
0.006 |
69.149 |
| SMC |
2 |
0.052 |
0.058 |
0.040 |
-0.148 |
| SMC |
3 |
0.041 |
0.052 |
0.033 |
-0.344 |
| SMC |
5 |
0.035 |
0.041 |
0.025 |
-0.233 |
| SMC |
8 |
0.032 |
0.035 |
0.016 |
-0.201 |
| SMC |
15 |
0.030 |
0.032 |
0.012 |
-0.195 |
| SMC |
30 |
0.030 |
0.028 |
0.006 |
0.448 |
| Metro |
2 |
0.559 |
0.058 |
0.040 |
12.532 |
| Metro |
3 |
0.408 |
0.052 |
0.033 |
10.683 |
| Metro |
5 |
0.333 |
0.041 |
0.025 |
11.656 |
| Metro |
8 |
0.256 |
0.035 |
0.016 |
14.236 |
| Metro |
15 |
0.190 |
0.032 |
0.012 |
13.637 |
| Metro |
30 |
0.131 |
0.028 |
0.006 |
17.867 |
| DEMetro_Z |
2 |
0.358 |
0.058 |
0.040 |
7.504 |
| DEMetro_Z |
3 |
1.006 |
0.052 |
0.033 |
28.645 |
| DEMetro_Z |
5 |
1.826 |
0.041 |
0.025 |
71.393 |
| DEMetro_Z |
8 |
6.129 |
0.035 |
0.016 |
392.464 |
| DEMetro_Z |
15 |
9.031 |
0.032 |
0.012 |
776.310 |
| DEMetro_Z |
30 |
11.181 |
0.028 |
0.006 |
1934.906 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
6.157 |
1.03e-06 |
75.732 |
| HMC |
3 |
5.811 |
2.67e-06 |
96.233 |
| HMC |
5 |
6.205 |
9.08e-07 |
100.668 |
| HMC |
8 |
7.342 |
4.33e-08 |
70.065 |
| HMC |
15 |
6.538 |
3.66e-07 |
54.711 |
| HMC |
30 |
5.995 |
1.61e-06 |
117.368 |
| SMC |
2 |
-0.028 |
0.978 |
-0.007 |
| SMC |
3 |
2.013 |
0.0493 |
0.642 |
| SMC |
5 |
0.875 |
0.386 |
0.257 |
| SMC |
8 |
-1.610 |
0.114 |
-0.354 |
| SMC |
15 |
-1.226 |
0.226 |
-0.265 |
| SMC |
30 |
1.899 |
0.0634 |
0.639 |
| Metro |
2 |
4.368 |
0.000142 |
8.966 |
| Metro |
3 |
3.450 |
0.00172 |
8.771 |
| Metro |
5 |
3.484 |
0.00157 |
7.907 |
| Metro |
8 |
3.740 |
0.000768 |
4.696 |
| Metro |
15 |
5.379 |
6.1e-06 |
3.916 |
| Metro |
30 |
3.710 |
0.000868 |
12.253 |
| DEMetro_Z |
2 |
3.616 |
0.00109 |
5.835 |
| DEMetro_Z |
3 |
4.444 |
0.000118 |
63.657 |
| DEMetro_Z |
5 |
4.932 |
3.06e-05 |
290.759 |
| DEMetro_Z |
8 |
9.831 |
9.69e-11 |
471.111 |
| DEMetro_Z |
15 |
15.229 |
2.27e-15 |
512.351 |
| DEMetro_Z |
30 |
14.302 |
1.14e-14 |
1807.703 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
6.155
|
1.04e-06
|
1.124
|
| HMC_vs_SMC |
1
|
5.754
|
3.13e-06
|
1.051
|
| HMC_vs_SMC |
2
|
6.206
|
9.06e-07
|
1.133
|
| HMC_vs_SMC |
3
|
7.368
|
4.07e-08
|
1.345
|
| HMC_vs_SMC |
4
|
6.565
|
3.42e-07
|
1.199
|
| HMC_vs_SMC |
5
|
5.973
|
1.72e-06
|
1.090
|
| Metro_vs_DEMetro_Z |
0
|
1.215
|
0.234
|
0.222
|
| Metro_vs_DEMetro_Z |
1
|
-3.848
|
0.000604
|
-0.702
|
| Metro_vs_DEMetro_Z |
2
|
-4.770
|
4.81e-05
|
-0.871
|
| Metro_vs_DEMetro_Z |
3
|
-9.754
|
1.16e-10
|
-1.781
|
| Metro_vs_DEMetro_Z |
4
|
-15.203
|
2.37e-15
|
-2.776
|
| Metro_vs_DEMetro_Z |
5
|
-14.172
|
1.44e-14
|
-2.587
|
| HMC_vs_Metro |
0
|
5.317
|
1.05e-05
|
0.971
|
| HMC_vs_Metro |
1
|
5.090
|
1.97e-05
|
0.929
|
| HMC_vs_Metro |
2
|
5.464
|
7e-06
|
0.998
|
| HMC_vs_Metro |
3
|
6.559
|
3.48e-07
|
1.198
|
| HMC_vs_Metro |
4
|
5.978
|
1.69e-06
|
1.092
|
| HMC_vs_Metro |
5
|
5.163
|
1.61e-05
|
0.943
|
| HMC_vs_DEMetro_Z |
0
|
5.865
|
2.31e-06
|
1.071
|
| HMC_vs_DEMetro_Z |
1
|
1.608
|
0.119
|
0.294
|
| HMC_vs_DEMetro_Z |
2
|
-3.243
|
0.00298
|
-0.592
|
| HMC_vs_DEMetro_Z |
3
|
-8.245
|
4.33e-09
|
-1.505
|
| HMC_vs_DEMetro_Z |
4
|
-13.731
|
3.21e-14
|
-2.507
|
| HMC_vs_DEMetro_Z |
5
|
-13.463
|
5.27e-14
|
-2.458
|
| Metro_vs_SMC |
0
|
4.433
|
0.000122
|
0.809
|
| Metro_vs_SMC |
1
|
3.152
|
0.00375
|
0.575
|
| Metro_vs_SMC |
2
|
3.299
|
0.00258
|
0.602
|
| Metro_vs_SMC |
3
|
4.009
|
0.00039
|
0.732
|
| Metro_vs_SMC |
4
|
5.788
|
2.86e-06
|
1.057
|
| Metro_vs_SMC |
5
|
3.508
|
0.00149
|
0.640
|
| DEMetro_Z_vs_SMC |
0
|
3.688
|
0.000928
|
0.673
|
| DEMetro_Z_vs_SMC |
1
|
4.413
|
0.000129
|
0.806
|
| DEMetro_Z_vs_SMC |
2
|
4.932
|
3.06e-05
|
0.900
|
| DEMetro_Z_vs_SMC |
3
|
9.841
|
9.48e-11
|
1.797
|
| DEMetro_Z_vs_SMC |
4
|
15.239
|
2.23e-15
|
2.782
|
| DEMetro_Z_vs_SMC |
5
|
14.311
|
1.12e-14
|
2.613
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
5.613 |
0.091 |
0.073 |
75.732 |
| HMC |
3 |
4.453 |
0.072 |
0.046 |
96.233 |
| HMC |
5 |
3.562 |
0.071 |
0.035 |
100.668 |
| HMC |
8 |
3.457 |
0.074 |
0.048 |
70.065 |
| HMC |
15 |
2.041 |
0.061 |
0.036 |
54.711 |
| HMC |
30 |
1.330 |
0.041 |
0.011 |
117.368 |
| SMC |
2 |
0.090 |
0.091 |
0.073 |
-0.007 |
| SMC |
3 |
0.102 |
0.072 |
0.046 |
0.642 |
| SMC |
5 |
0.080 |
0.071 |
0.035 |
0.257 |
| SMC |
8 |
0.057 |
0.074 |
0.048 |
-0.354 |
| SMC |
15 |
0.051 |
0.061 |
0.036 |
-0.265 |
| SMC |
30 |
0.048 |
0.041 |
0.011 |
0.639 |
| Metro |
2 |
0.744 |
0.091 |
0.073 |
8.966 |
| Metro |
3 |
0.472 |
0.072 |
0.046 |
8.771 |
| Metro |
5 |
0.345 |
0.071 |
0.035 |
7.907 |
| Metro |
8 |
0.301 |
0.074 |
0.048 |
4.696 |
| Metro |
15 |
0.202 |
0.061 |
0.036 |
3.916 |
| Metro |
30 |
0.176 |
0.041 |
0.011 |
12.253 |
| DEMetro_Z |
2 |
0.516 |
0.091 |
0.073 |
5.835 |
| DEMetro_Z |
3 |
2.970 |
0.072 |
0.046 |
63.657 |
| DEMetro_Z |
5 |
10.153 |
0.071 |
0.035 |
290.759 |
| DEMetro_Z |
8 |
22.820 |
0.074 |
0.048 |
471.111 |
| DEMetro_Z |
15 |
18.609 |
0.061 |
0.036 |
512.351 |
| DEMetro_Z |
30 |
19.895 |
0.041 |
0.011 |
1807.703 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
8.285 |
3.85e-09 |
47.192 |
| HMC |
3 |
7.912 |
9.86e-09 |
43.024 |
| HMC |
5 |
8.694 |
1.4e-09 |
44.742 |
| HMC |
8 |
9.728 |
1.22e-10 |
74.423 |
| HMC |
15 |
8.844 |
9.82e-10 |
70.024 |
| HMC |
30 |
8.381 |
3.07e-09 |
90.289 |
| SMC |
2 |
-0.632 |
0.53 |
-0.147 |
| SMC |
3 |
-1.148 |
0.256 |
-0.257 |
| SMC |
5 |
-1.104 |
0.275 |
-0.247 |
| SMC |
8 |
-1.183 |
0.242 |
-0.275 |
| SMC |
15 |
-0.559 |
0.579 |
-0.132 |
| SMC |
30 |
1.866 |
0.0675 |
0.564 |
| Metro |
2 |
6.252 |
7.6e-07 |
14.887 |
| Metro |
3 |
5.888 |
2.04e-06 |
12.099 |
| Metro |
5 |
7.239 |
4.99e-08 |
12.463 |
| Metro |
8 |
6.948 |
1.16e-07 |
17.561 |
| Metro |
15 |
8.531 |
1.86e-09 |
16.923 |
| Metro |
30 |
5.755 |
3.08e-06 |
22.418 |
| DEMetro_Z |
2 |
4.551 |
8.55e-05 |
9.336 |
| DEMetro_Z |
3 |
6.353 |
6e-07 |
31.823 |
| DEMetro_Z |
5 |
10.627 |
1.61e-11 |
85.833 |
| DEMetro_Z |
8 |
11.815 |
1.32e-12 |
518.211 |
| DEMetro_Z |
15 |
18.331 |
1.72e-17 |
1090.155 |
| DEMetro_Z |
30 |
33.227 |
1.23e-24 |
2683.139 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
1.795
|
0.0831
|
0.328
|
| Metro_vs_DEMetro_Z |
1
|
-3.815
|
0.00066
|
-0.696
|
| Metro_vs_DEMetro_Z |
2
|
-9.039
|
6.2e-10
|
-1.650
|
| Metro_vs_DEMetro_Z |
3
|
-11.403
|
3.1e-12
|
-2.082
|
| Metro_vs_DEMetro_Z |
4
|
-18.327
|
1.73e-17
|
-3.346
|
| Metro_vs_DEMetro_Z |
5
|
-33.028
|
1.46e-24
|
-6.030
|
| DEMetro_Z_vs_SMC |
0
|
4.612
|
7.44e-05
|
0.842
|
| DEMetro_Z_vs_SMC |
1
|
6.407
|
5.25e-07
|
1.170
|
| DEMetro_Z_vs_SMC |
2
|
10.630
|
1.62e-11
|
1.941
|
| DEMetro_Z_vs_SMC |
3
|
11.828
|
1.29e-12
|
2.159
|
| DEMetro_Z_vs_SMC |
4
|
18.339
|
1.7e-17
|
3.348
|
| DEMetro_Z_vs_SMC |
5
|
33.217
|
1.24e-24
|
6.065
|
| HMC_vs_DEMetro_Z |
0
|
6.466
|
4.47e-07
|
1.181
|
| HMC_vs_DEMetro_Z |
1
|
1.593
|
0.122
|
0.291
|
| HMC_vs_DEMetro_Z |
2
|
-4.213
|
0.000224
|
-0.769
|
| HMC_vs_DEMetro_Z |
3
|
-10.077
|
5.55e-11
|
-1.840
|
| HMC_vs_DEMetro_Z |
4
|
-16.782
|
1.8e-16
|
-3.064
|
| HMC_vs_DEMetro_Z |
5
|
-31.113
|
7.88e-24
|
-5.680
|
| HMC_vs_Metro |
0
|
5.042
|
2.26e-05
|
0.921
|
| HMC_vs_Metro |
1
|
5.011
|
2.46e-05
|
0.915
|
| HMC_vs_Metro |
2
|
5.672
|
3.94e-06
|
1.035
|
| HMC_vs_Metro |
3
|
6.574
|
3.34e-07
|
1.200
|
| HMC_vs_Metro |
4
|
6.349
|
6.14e-07
|
1.159
|
| HMC_vs_Metro |
5
|
5.563
|
5.31e-06
|
1.016
|
| HMC_vs_SMC |
0
|
8.285
|
3.91e-09
|
1.513
|
| HMC_vs_SMC |
1
|
7.982
|
8.39e-09
|
1.457
|
| HMC_vs_SMC |
2
|
8.779
|
1.16e-09
|
1.603
|
| HMC_vs_SMC |
3
|
9.741
|
1.19e-10
|
1.778
|
| HMC_vs_SMC |
4
|
8.775
|
1.17e-09
|
1.602
|
| HMC_vs_SMC |
5
|
8.372
|
3.16e-09
|
1.528
|
| Metro_vs_SMC |
0
|
6.206
|
9.05e-07
|
1.133
|
| Metro_vs_SMC |
1
|
6.017
|
1.52e-06
|
1.099
|
| Metro_vs_SMC |
2
|
7.286
|
5.03e-08
|
1.330
|
| Metro_vs_SMC |
3
|
7.059
|
9.16e-08
|
1.289
|
| Metro_vs_SMC |
4
|
8.733
|
1.3e-09
|
1.594
|
| Metro_vs_SMC |
5
|
5.540
|
5.66e-06
|
1.011
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
1.492 |
0.069 |
0.030 |
47.192 |
| HMC |
3 |
1.152 |
0.059 |
0.025 |
43.024 |
| HMC |
5 |
0.891 |
0.050 |
0.019 |
44.742 |
| HMC |
8 |
0.796 |
0.043 |
0.010 |
74.423 |
| HMC |
15 |
0.528 |
0.038 |
0.007 |
70.024 |
| HMC |
30 |
0.345 |
0.034 |
0.003 |
90.289 |
| SMC |
2 |
0.064 |
0.069 |
0.030 |
-0.147 |
| SMC |
3 |
0.053 |
0.059 |
0.025 |
-0.257 |
| SMC |
5 |
0.045 |
0.050 |
0.019 |
-0.247 |
| SMC |
8 |
0.040 |
0.043 |
0.010 |
-0.275 |
| SMC |
15 |
0.037 |
0.038 |
0.007 |
-0.132 |
| SMC |
30 |
0.036 |
0.034 |
0.003 |
0.564 |
| Metro |
2 |
0.518 |
0.069 |
0.030 |
14.887 |
| Metro |
3 |
0.367 |
0.059 |
0.025 |
12.099 |
| Metro |
5 |
0.284 |
0.050 |
0.019 |
12.463 |
| Metro |
8 |
0.221 |
0.043 |
0.010 |
17.561 |
| Metro |
15 |
0.157 |
0.038 |
0.007 |
16.923 |
| Metro |
30 |
0.111 |
0.034 |
0.003 |
22.418 |
| DEMetro_Z |
2 |
0.350 |
0.069 |
0.030 |
9.336 |
| DEMetro_Z |
3 |
0.868 |
0.059 |
0.025 |
31.823 |
| DEMetro_Z |
5 |
1.664 |
0.050 |
0.019 |
85.833 |
| DEMetro_Z |
8 |
5.284 |
0.043 |
0.010 |
518.211 |
| DEMetro_Z |
15 |
7.661 |
0.038 |
0.007 |
1090.155 |
| DEMetro_Z |
30 |
9.271 |
0.034 |
0.003 |
2683.139 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
8.361 |
3.19e-09 |
51.989 |
| HMC |
3 |
7.844 |
1.17e-08 |
43.389 |
| HMC |
5 |
8.688 |
1.42e-09 |
48.008 |
| HMC |
8 |
9.769 |
1.11e-10 |
74.063 |
| HMC |
15 |
9.088 |
5.45e-10 |
61.346 |
| HMC |
30 |
8.447 |
2.61e-09 |
80.880 |
| SMC |
2 |
-0.451 |
0.653 |
-0.109 |
| SMC |
3 |
-1.021 |
0.312 |
-0.229 |
| SMC |
5 |
-1.230 |
0.224 |
-0.275 |
| SMC |
8 |
-1.102 |
0.275 |
-0.277 |
| SMC |
15 |
-0.802 |
0.426 |
-0.184 |
| SMC |
30 |
1.556 |
0.126 |
0.458 |
| Metro |
2 |
6.315 |
6.44e-07 |
15.972 |
| Metro |
3 |
5.989 |
1.53e-06 |
11.496 |
| Metro |
5 |
7.241 |
4.98e-08 |
12.768 |
| Metro |
8 |
6.809 |
1.67e-07 |
16.398 |
| Metro |
15 |
8.537 |
1.76e-09 |
15.086 |
| Metro |
30 |
5.686 |
3.71e-06 |
20.241 |
| DEMetro_Z |
2 |
4.441 |
0.000117 |
9.782 |
| DEMetro_Z |
3 |
6.109 |
1.17e-06 |
31.276 |
| DEMetro_Z |
5 |
13.959 |
1.96e-14 |
55.160 |
| DEMetro_Z |
8 |
31.146 |
7e-24 |
165.944 |
| DEMetro_Z |
15 |
65.303 |
3.54e-33 |
221.365 |
| DEMetro_Z |
30 |
73.202 |
1.62e-34 |
408.479 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.484
|
0.000106
|
0.819
|
| DEMetro_Z_vs_SMC |
1
|
6.148
|
1.06e-06
|
1.122
|
| DEMetro_Z_vs_SMC |
2
|
13.988
|
2.01e-14
|
2.554
|
| DEMetro_Z_vs_SMC |
3
|
31.358
|
6.32e-24
|
5.725
|
| DEMetro_Z_vs_SMC |
4
|
65.605
|
4.36e-33
|
11.978
|
| DEMetro_Z_vs_SMC |
5
|
72.564
|
2.38e-34
|
13.248
|
| HMC_vs_Metro |
0
|
5.196
|
1.47e-05
|
0.949
|
| HMC_vs_Metro |
1
|
5.189
|
1.5e-05
|
0.947
|
| HMC_vs_Metro |
2
|
5.722
|
3.43e-06
|
1.045
|
| HMC_vs_Metro |
3
|
6.746
|
2.11e-07
|
1.232
|
| HMC_vs_Metro |
4
|
6.404
|
5.29e-07
|
1.169
|
| HMC_vs_Metro |
5
|
5.581
|
5.05e-06
|
1.019
|
| Metro_vs_DEMetro_Z |
0
|
1.919
|
0.0649
|
0.350
|
| Metro_vs_DEMetro_Z |
1
|
-3.765
|
0.000755
|
-0.687
|
| Metro_vs_DEMetro_Z |
2
|
-10.906
|
8.91e-12
|
-1.991
|
| Metro_vs_DEMetro_Z |
3
|
-24.884
|
4.09e-21
|
-4.543
|
| Metro_vs_DEMetro_Z |
4
|
-68.057
|
1.52e-33
|
-12.425
|
| Metro_vs_DEMetro_Z |
5
|
-58.090
|
1.45e-31
|
-10.606
|
| HMC_vs_SMC |
0
|
8.358
|
3.26e-09
|
1.526
|
| HMC_vs_SMC |
1
|
7.914
|
9.96e-09
|
1.445
|
| HMC_vs_SMC |
2
|
8.760
|
1.22e-09
|
1.599
|
| HMC_vs_SMC |
3
|
9.770
|
1.12e-10
|
1.784
|
| HMC_vs_SMC |
4
|
9.013
|
6.61e-10
|
1.645
|
| HMC_vs_SMC |
5
|
8.422
|
2.79e-09
|
1.538
|
| Metro_vs_SMC |
0
|
6.250
|
8.04e-07
|
1.141
|
| Metro_vs_SMC |
1
|
6.097
|
1.22e-06
|
1.113
|
| Metro_vs_SMC |
2
|
7.287
|
5.02e-08
|
1.330
|
| Metro_vs_SMC |
3
|
6.939
|
1.26e-07
|
1.267
|
| Metro_vs_SMC |
4
|
8.736
|
1.29e-09
|
1.595
|
| Metro_vs_SMC |
5
|
5.495
|
6.42e-06
|
1.003
|
| HMC_vs_DEMetro_Z |
0
|
6.487
|
4.22e-07
|
1.184
|
| HMC_vs_DEMetro_Z |
1
|
1.721
|
0.0958
|
0.314
|
| HMC_vs_DEMetro_Z |
2
|
-1.119
|
0.272
|
-0.204
|
| HMC_vs_DEMetro_Z |
3
|
-10.159
|
4.61e-11
|
-1.855
|
| HMC_vs_DEMetro_Z |
4
|
-20.124
|
1.39e-18
|
-3.674
|
| HMC_vs_DEMetro_Z |
5
|
-27.483
|
2.57e-22
|
-5.018
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.366 |
0.013 |
0.007 |
51.989 |
| HMC |
3 |
0.348 |
0.014 |
0.008 |
43.389 |
| HMC |
5 |
0.333 |
0.014 |
0.007 |
48.008 |
| HMC |
8 |
0.352 |
0.014 |
0.005 |
74.063 |
| HMC |
15 |
0.263 |
0.014 |
0.004 |
61.346 |
| HMC |
30 |
0.199 |
0.014 |
0.002 |
80.880 |
| SMC |
2 |
0.012 |
0.013 |
0.007 |
-0.109 |
| SMC |
3 |
0.012 |
0.014 |
0.008 |
-0.229 |
| SMC |
5 |
0.012 |
0.014 |
0.007 |
-0.275 |
| SMC |
8 |
0.013 |
0.014 |
0.005 |
-0.277 |
| SMC |
15 |
0.014 |
0.014 |
0.004 |
-0.184 |
| SMC |
30 |
0.015 |
0.014 |
0.002 |
0.458 |
| Metro |
2 |
0.122 |
0.013 |
0.007 |
15.972 |
| Metro |
3 |
0.102 |
0.014 |
0.008 |
11.496 |
| Metro |
5 |
0.099 |
0.014 |
0.007 |
12.768 |
| Metro |
8 |
0.089 |
0.014 |
0.005 |
16.398 |
| Metro |
15 |
0.075 |
0.014 |
0.004 |
15.086 |
| Metro |
30 |
0.060 |
0.014 |
0.002 |
20.241 |
| DEMetro_Z |
2 |
0.079 |
0.013 |
0.007 |
9.782 |
| DEMetro_Z |
3 |
0.254 |
0.014 |
0.008 |
31.276 |
| DEMetro_Z |
5 |
0.380 |
0.014 |
0.007 |
55.160 |
| DEMetro_Z |
8 |
0.771 |
0.014 |
0.005 |
165.944 |
| DEMetro_Z |
15 |
0.910 |
0.014 |
0.004 |
221.365 |
| DEMetro_Z |
30 |
0.947 |
0.014 |
0.002 |
408.479 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_high_Dimension
(Mixture,
mm,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
-6.986 |
3.5e-09 |
-1.673 |
| HMC |
4 |
-0.376 |
0.709 |
-0.131 |
| HMC |
6 |
5.947 |
1.72e-06 |
11.545 |
| HMC |
8 |
6.506 |
3.97e-07 |
36.222 |
| HMC |
10 |
4.791 |
4.52e-05 |
29.689 |
| HMC |
12 |
5.652 |
4.14e-06 |
38.971 |
| SMC |
0 |
1.363 |
0.178 |
0.377 |
| SMC |
4 |
1.672 |
0.0998 |
0.430 |
| SMC |
6 |
0.774 |
0.443 |
0.265 |
| SMC |
8 |
1.689 |
0.097 |
0.523 |
| SMC |
10 |
-0.468 |
0.641 |
-0.119 |
| SMC |
12 |
0.868 |
0.39 |
0.279 |
| Metro |
0 |
15.884 |
1.28e-19 |
6.394 |
| Metro |
4 |
13.874 |
1.43e-17 |
5.516 |
| Metro |
6 |
7.334 |
3.24e-08 |
8.306 |
| Metro |
8 |
7.187 |
6.35e-08 |
26.744 |
| Metro |
10 |
6.829 |
1.67e-07 |
35.289 |
| Metro |
12 |
5.947 |
1.83e-06 |
37.425 |
| DEMetro_Z |
0 |
33.756 |
7.88e-25 |
2716.720 |
| DEMetro_Z |
4 |
40.746 |
3.74e-27 |
2061.767 |
| DEMetro_Z |
6 |
40.112 |
5.85e-27 |
1898.382 |
| DEMetro_Z |
8 |
41.062 |
3e-27 |
1245.866 |
| DEMetro_Z |
10 |
51.607 |
4.27e-30 |
774.966 |
| DEMetro_Z |
12 |
41.324 |
2.48e-27 |
665.002 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-33.769
|
7.79e-25
|
-6.165
|
| HMC_vs_DEMetro_Z |
1
|
-40.706
|
3.85e-27
|
-7.432
|
| HMC_vs_DEMetro_Z |
2
|
-39.532
|
8.88e-27
|
-7.218
|
| HMC_vs_DEMetro_Z |
3
|
-40.347
|
4.96e-27
|
-7.366
|
| HMC_vs_DEMetro_Z |
4
|
-44.144
|
3.81e-28
|
-8.059
|
| HMC_vs_DEMetro_Z |
5
|
-41.041
|
3.05e-27
|
-7.493
|
| Metro_vs_SMC |
0
|
16.488
|
2.86e-16
|
3.010
|
| Metro_vs_SMC |
1
|
12.641
|
2.53e-13
|
2.308
|
| Metro_vs_SMC |
2
|
7.222
|
5.96e-08
|
1.319
|
| Metro_vs_SMC |
3
|
7.108
|
8.05e-08
|
1.298
|
| Metro_vs_SMC |
4
|
6.924
|
1.31e-07
|
1.264
|
| Metro_vs_SMC |
5
|
5.930
|
1.93e-06
|
1.083
|
| Metro_vs_DEMetro_Z |
0
|
-33.646
|
8.64e-25
|
-6.143
|
| Metro_vs_DEMetro_Z |
1
|
-40.696
|
3.88e-27
|
-7.430
|
| Metro_vs_DEMetro_Z |
2
|
-39.794
|
7.35e-27
|
-7.265
|
| Metro_vs_DEMetro_Z |
3
|
-39.809
|
7.28e-27
|
-7.268
|
| Metro_vs_DEMetro_Z |
4
|
-44.023
|
4.12e-28
|
-8.037
|
| Metro_vs_DEMetro_Z |
5
|
-39.785
|
7.4e-27
|
-7.264
|
| HMC_vs_Metro |
0
|
-22.194
|
9.6e-20
|
-4.052
|
| HMC_vs_Metro |
1
|
-13.729
|
3.22e-14
|
-2.507
|
| HMC_vs_Metro |
2
|
1.382
|
0.177
|
0.252
|
| HMC_vs_Metro |
3
|
1.396
|
0.173
|
0.255
|
| HMC_vs_Metro |
4
|
-0.933
|
0.359
|
-0.170
|
| HMC_vs_Metro |
5
|
0.407
|
0.687
|
0.074
|
| HMC_vs_SMC |
0
|
-9.670
|
1.41e-10
|
-1.765
|
| HMC_vs_SMC |
1
|
-1.714
|
0.0971
|
-0.313
|
| HMC_vs_SMC |
2
|
5.764
|
3.05e-06
|
1.052
|
| HMC_vs_SMC |
3
|
6.390
|
5.49e-07
|
1.167
|
| HMC_vs_SMC |
4
|
4.847
|
3.88e-05
|
0.885
|
| HMC_vs_SMC |
5
|
5.633
|
4.38e-06
|
1.028
|
| DEMetro_Z_vs_SMC |
0
|
33.751
|
7.91e-25
|
6.162
|
| DEMetro_Z_vs_SMC |
1
|
40.713
|
3.84e-27
|
7.433
|
| DEMetro_Z_vs_SMC |
2
|
40.021
|
6.25e-27
|
7.307
|
| DEMetro_Z_vs_SMC |
3
|
41.162
|
2.81e-27
|
7.515
|
| DEMetro_Z_vs_SMC |
4
|
51.529
|
4.53e-30
|
9.408
|
| DEMetro_Z_vs_SMC |
5
|
41.403
|
2.37e-27
|
7.559
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.018 |
0.022 |
0.002 |
-1.673 |
| HMC |
4 |
0.023 |
0.023 |
0.003 |
-0.131 |
| HMC |
6 |
0.065 |
0.025 |
0.003 |
11.545 |
| HMC |
8 |
0.213 |
0.026 |
0.005 |
36.222 |
| HMC |
10 |
0.270 |
0.029 |
0.008 |
29.689 |
| HMC |
12 |
0.408 |
0.031 |
0.010 |
38.971 |
| SMC |
0 |
0.023 |
0.022 |
0.002 |
0.377 |
| SMC |
4 |
0.025 |
0.023 |
0.003 |
0.430 |
| SMC |
6 |
0.026 |
0.025 |
0.003 |
0.265 |
| SMC |
8 |
0.029 |
0.026 |
0.005 |
0.523 |
| SMC |
10 |
0.028 |
0.029 |
0.008 |
-0.119 |
| SMC |
12 |
0.034 |
0.031 |
0.010 |
0.279 |
| Metro |
0 |
0.037 |
0.022 |
0.002 |
6.394 |
| Metro |
4 |
0.041 |
0.023 |
0.003 |
5.516 |
| Metro |
6 |
0.054 |
0.025 |
0.003 |
8.306 |
| Metro |
8 |
0.164 |
0.026 |
0.005 |
26.744 |
| Metro |
10 |
0.315 |
0.029 |
0.008 |
35.289 |
| Metro |
12 |
0.393 |
0.031 |
0.010 |
37.425 |
| DEMetro_Z |
0 |
6.531 |
0.022 |
0.002 |
2716.720 |
| DEMetro_Z |
4 |
6.740 |
0.023 |
0.003 |
2061.767 |
| DEMetro_Z |
6 |
6.623 |
0.025 |
0.003 |
1898.382 |
| DEMetro_Z |
8 |
6.469 |
0.026 |
0.005 |
1245.866 |
| DEMetro_Z |
10 |
6.314 |
0.029 |
0.008 |
774.966 |
| DEMetro_Z |
12 |
6.465 |
0.031 |
0.010 |
665.002 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
9.943 |
6.58e-14 |
2.917 |
| HMC |
4 |
4.433 |
4.58e-05 |
1.017 |
| HMC |
6 |
4.016 |
0.000223 |
1.532 |
| HMC |
8 |
4.084 |
0.000317 |
20.418 |
| HMC |
10 |
3.746 |
0.000792 |
59.976 |
| HMC |
12 |
4.233 |
0.000212 |
106.223 |
| SMC |
0 |
2.929 |
0.0049 |
0.832 |
| SMC |
4 |
4.308 |
8e-05 |
1.491 |
| SMC |
6 |
2.366 |
0.0219 |
0.798 |
| SMC |
8 |
2.113 |
0.039 |
0.593 |
| SMC |
10 |
2.398 |
0.0213 |
1.092 |
| SMC |
12 |
3.863 |
0.000371 |
1.550 |
| Metro |
0 |
16.403 |
8.54e-23 |
4.865 |
| Metro |
4 |
13.326 |
3.19e-19 |
3.622 |
| Metro |
6 |
6.805 |
6.83e-09 |
1.901 |
| Metro |
8 |
4.270 |
0.000188 |
11.440 |
| Metro |
10 |
5.002 |
2.52e-05 |
61.092 |
| Metro |
12 |
4.146 |
0.000269 |
95.038 |
| DEMetro_Z |
0 |
36.992 |
5.87e-26 |
42378.668 |
| DEMetro_Z |
4 |
37.271 |
4.75e-26 |
25311.282 |
| DEMetro_Z |
6 |
46.109 |
1.09e-28 |
13873.444 |
| DEMetro_Z |
8 |
40.318 |
5.06e-27 |
9812.353 |
| DEMetro_Z |
10 |
29.819 |
2.61e-23 |
12268.492 |
| DEMetro_Z |
12 |
32.340 |
2.65e-24 |
11072.193 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
7.274
|
5.2e-08
|
1.328
|
| HMC_vs_SMC |
1
|
-1.294
|
0.206
|
-0.236
|
| HMC_vs_SMC |
2
|
1.948
|
0.0612
|
0.356
|
| HMC_vs_SMC |
3
|
4.031
|
0.000368
|
0.736
|
| HMC_vs_SMC |
4
|
3.669
|
0.000976
|
0.670
|
| HMC_vs_SMC |
5
|
4.156
|
0.000262
|
0.759
|
| Metro_vs_DEMetro_Z |
0
|
-36.987
|
5.9e-26
|
-6.753
|
| Metro_vs_DEMetro_Z |
1
|
-37.265
|
4.77e-26
|
-6.804
|
| Metro_vs_DEMetro_Z |
2
|
-46.099
|
1.1e-28
|
-8.417
|
| Metro_vs_DEMetro_Z |
3
|
-40.156
|
5.68e-27
|
-7.332
|
| Metro_vs_DEMetro_Z |
4
|
-29.491
|
3.56e-23
|
-5.384
|
| Metro_vs_DEMetro_Z |
5
|
-31.569
|
5.23e-24
|
-5.764
|
| HMC_vs_Metro |
0
|
-5.498
|
6.37e-06
|
-1.004
|
| HMC_vs_Metro |
1
|
-11.672
|
1.77e-12
|
-2.131
|
| HMC_vs_Metro |
2
|
-1.043
|
0.306
|
-0.190
|
| HMC_vs_Metro |
3
|
1.566
|
0.128
|
0.286
|
| HMC_vs_Metro |
4
|
-0.070
|
0.945
|
-0.013
|
| HMC_vs_Metro |
5
|
1.073
|
0.292
|
0.196
|
| HMC_vs_DEMetro_Z |
0
|
-36.989
|
5.89e-26
|
-6.753
|
| HMC_vs_DEMetro_Z |
1
|
-37.269
|
4.75e-26
|
-6.804
|
| HMC_vs_DEMetro_Z |
2
|
-46.091
|
1.11e-28
|
-8.415
|
| HMC_vs_DEMetro_Z |
3
|
-40.080
|
6e-27
|
-7.318
|
| HMC_vs_DEMetro_Z |
4
|
-29.403
|
3.87e-23
|
-5.368
|
| HMC_vs_DEMetro_Z |
5
|
-31.674
|
4.76e-24
|
-5.783
|
| Metro_vs_SMC |
0
|
11.236
|
4.41e-12
|
2.051
|
| Metro_vs_SMC |
1
|
6.876
|
1.49e-07
|
1.255
|
| Metro_vs_SMC |
2
|
3.167
|
0.00361
|
0.578
|
| Metro_vs_SMC |
3
|
4.086
|
0.000316
|
0.746
|
| Metro_vs_SMC |
4
|
4.951
|
2.9e-05
|
0.904
|
| Metro_vs_SMC |
5
|
4.059
|
0.00034
|
0.741
|
| DEMetro_Z_vs_SMC |
0
|
36.991
|
5.88e-26
|
6.754
|
| DEMetro_Z_vs_SMC |
1
|
37.268
|
4.75e-26
|
6.804
|
| DEMetro_Z_vs_SMC |
2
|
46.102
|
1.1e-28
|
8.417
|
| DEMetro_Z_vs_SMC |
3
|
40.316
|
5.07e-27
|
7.361
|
| DEMetro_Z_vs_SMC |
4
|
29.817
|
2.61e-23
|
5.444
|
| DEMetro_Z_vs_SMC |
5
|
32.339
|
2.65e-24
|
5.904
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.043 |
0.032 |
0.004 |
2.917 |
| HMC |
4 |
0.043 |
0.036 |
0.007 |
1.017 |
| HMC |
6 |
0.060 |
0.041 |
0.013 |
1.532 |
| HMC |
8 |
0.386 |
0.045 |
0.017 |
20.418 |
| HMC |
10 |
0.833 |
0.046 |
0.013 |
59.976 |
| HMC |
12 |
1.662 |
0.044 |
0.015 |
106.223 |
| SMC |
0 |
0.035 |
0.032 |
0.004 |
0.832 |
| SMC |
4 |
0.046 |
0.036 |
0.007 |
1.491 |
| SMC |
6 |
0.051 |
0.041 |
0.013 |
0.798 |
| SMC |
8 |
0.055 |
0.045 |
0.017 |
0.593 |
| SMC |
10 |
0.060 |
0.046 |
0.013 |
1.092 |
| SMC |
12 |
0.067 |
0.044 |
0.015 |
1.550 |
| Metro |
0 |
0.051 |
0.032 |
0.004 |
4.865 |
| Metro |
4 |
0.060 |
0.036 |
0.007 |
3.622 |
| Metro |
6 |
0.065 |
0.041 |
0.013 |
1.901 |
| Metro |
8 |
0.236 |
0.045 |
0.017 |
11.440 |
| Metro |
10 |
0.848 |
0.046 |
0.013 |
61.092 |
| Metro |
12 |
1.491 |
0.044 |
0.015 |
95.038 |
| DEMetro_Z |
0 |
173.169 |
0.032 |
0.004 |
42378.668 |
| DEMetro_Z |
4 |
166.466 |
0.036 |
0.007 |
25311.282 |
| DEMetro_Z |
6 |
175.050 |
0.041 |
0.013 |
13873.444 |
| DEMetro_Z |
8 |
164.046 |
0.045 |
0.017 |
9812.353 |
| DEMetro_Z |
10 |
161.048 |
0.046 |
0.013 |
12268.492 |
| DEMetro_Z |
12 |
168.699 |
0.044 |
0.015 |
11072.193 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
-0.443 |
0.659 |
-0.101 |
| HMC |
4 |
2.330 |
0.0241 |
0.823 |
| HMC |
6 |
6.094 |
1.16e-06 |
12.761 |
| HMC |
8 |
6.358 |
5.96e-07 |
45.618 |
| HMC |
10 |
4.840 |
3.95e-05 |
39.048 |
| HMC |
12 |
5.722 |
3.42e-06 |
47.817 |
| SMC |
0 |
2.688 |
0.00943 |
0.769 |
| SMC |
4 |
2.988 |
0.00411 |
0.795 |
| SMC |
6 |
2.167 |
0.0349 |
0.709 |
| SMC |
8 |
2.113 |
0.0396 |
0.708 |
| SMC |
10 |
0.247 |
0.806 |
0.064 |
| SMC |
12 |
1.276 |
0.208 |
0.425 |
| Metro |
0 |
16.607 |
2.41e-19 |
7.722 |
| Metro |
4 |
16.255 |
5.38e-19 |
7.594 |
| Metro |
6 |
7.305 |
3.81e-08 |
9.675 |
| Metro |
8 |
6.988 |
1.09e-07 |
34.286 |
| Metro |
10 |
6.750 |
2.07e-07 |
45.083 |
| Metro |
12 |
5.992 |
1.62e-06 |
45.791 |
| DEMetro_Z |
0 |
63.569 |
1.08e-32 |
6844.797 |
| DEMetro_Z |
4 |
68.720 |
1.14e-33 |
5718.278 |
| DEMetro_Z |
6 |
65.446 |
4.67e-33 |
4521.960 |
| DEMetro_Z |
8 |
73.407 |
1.7e-34 |
3204.066 |
| DEMetro_Z |
10 |
62.858 |
1.49e-32 |
1940.523 |
| DEMetro_Z |
12 |
61.128 |
3.32e-32 |
1573.881 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-63.451
|
1.14e-32
|
-11.585
|
| Metro_vs_DEMetro_Z |
1
|
-68.625
|
1.19e-33
|
-12.529
|
| Metro_vs_DEMetro_Z |
2
|
-65.018
|
5.65e-33
|
-11.871
|
| Metro_vs_DEMetro_Z |
3
|
-71.765
|
3.28e-34
|
-13.102
|
| Metro_vs_DEMetro_Z |
4
|
-58.669
|
1.09e-31
|
-10.711
|
| Metro_vs_DEMetro_Z |
5
|
-57.594
|
1.85e-31
|
-10.515
|
| DEMetro_Z_vs_SMC |
0
|
63.522
|
1.11e-32
|
11.597
|
| DEMetro_Z_vs_SMC |
1
|
68.697
|
1.16e-33
|
12.542
|
| DEMetro_Z_vs_SMC |
2
|
65.430
|
4.71e-33
|
11.946
|
| DEMetro_Z_vs_SMC |
3
|
73.531
|
1.63e-34
|
13.425
|
| DEMetro_Z_vs_SMC |
4
|
62.839
|
1.51e-32
|
11.473
|
| DEMetro_Z_vs_SMC |
5
|
61.083
|
3.41e-32
|
11.152
|
| HMC_vs_DEMetro_Z |
0
|
-63.539
|
1.1e-32
|
-11.601
|
| HMC_vs_DEMetro_Z |
1
|
-68.642
|
1.18e-33
|
-12.532
|
| HMC_vs_DEMetro_Z |
2
|
-64.710
|
6.48e-33
|
-11.814
|
| HMC_vs_DEMetro_Z |
3
|
-70.046
|
6.6e-34
|
-12.789
|
| HMC_vs_DEMetro_Z |
4
|
-55.858
|
4.47e-31
|
-10.198
|
| HMC_vs_DEMetro_Z |
5
|
-61.428
|
2.9e-32
|
-11.215
|
| HMC_vs_Metro |
0
|
-17.886
|
3.31e-17
|
-3.266
|
| HMC_vs_Metro |
1
|
-14.943
|
3.71e-15
|
-2.728
|
| HMC_vs_Metro |
2
|
1.170
|
0.252
|
0.214
|
| HMC_vs_Metro |
3
|
1.288
|
0.208
|
0.235
|
| HMC_vs_Metro |
4
|
-0.768
|
0.449
|
-0.140
|
| HMC_vs_Metro |
5
|
0.430
|
0.67
|
0.079
|
| HMC_vs_SMC |
0
|
-4.343
|
0.000157
|
-0.793
|
| HMC_vs_SMC |
1
|
0.077
|
0.939
|
0.014
|
| HMC_vs_SMC |
2
|
5.719
|
3.45e-06
|
1.044
|
| HMC_vs_SMC |
3
|
6.249
|
8.06e-07
|
1.141
|
| HMC_vs_SMC |
4
|
4.854
|
3.8e-05
|
0.886
|
| HMC_vs_SMC |
5
|
5.685
|
3.79e-06
|
1.038
|
| Metro_vs_SMC |
0
|
16.493
|
2.84e-16
|
3.011
|
| Metro_vs_SMC |
1
|
13.771
|
2.98e-14
|
2.514
|
| Metro_vs_SMC |
2
|
6.851
|
1.59e-07
|
1.251
|
| Metro_vs_SMC |
3
|
6.874
|
1.49e-07
|
1.255
|
| Metro_vs_SMC |
4
|
6.787
|
1.89e-07
|
1.239
|
| Metro_vs_SMC |
5
|
5.952
|
1.82e-06
|
1.087
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.028 |
0.029 |
0.001 |
-0.101 |
| HMC |
4 |
0.031 |
0.030 |
0.002 |
0.823 |
| HMC |
6 |
0.061 |
0.032 |
0.002 |
12.761 |
| HMC |
8 |
0.175 |
0.034 |
0.003 |
45.618 |
| HMC |
10 |
0.230 |
0.036 |
0.005 |
39.048 |
| HMC |
12 |
0.335 |
0.038 |
0.006 |
47.817 |
| SMC |
0 |
0.030 |
0.029 |
0.001 |
0.769 |
| SMC |
4 |
0.031 |
0.030 |
0.002 |
0.795 |
| SMC |
6 |
0.034 |
0.032 |
0.002 |
0.709 |
| SMC |
8 |
0.036 |
0.034 |
0.003 |
0.708 |
| SMC |
10 |
0.036 |
0.036 |
0.005 |
0.064 |
| SMC |
12 |
0.041 |
0.038 |
0.006 |
0.425 |
| Metro |
0 |
0.040 |
0.029 |
0.001 |
7.722 |
| Metro |
4 |
0.043 |
0.030 |
0.002 |
7.594 |
| Metro |
6 |
0.054 |
0.032 |
0.002 |
9.675 |
| Metro |
8 |
0.140 |
0.034 |
0.003 |
34.286 |
| Metro |
10 |
0.260 |
0.036 |
0.005 |
45.083 |
| Metro |
12 |
0.323 |
0.038 |
0.006 |
45.791 |
| DEMetro_Z |
0 |
10.261 |
0.029 |
0.001 |
6844.797 |
| DEMetro_Z |
4 |
10.143 |
0.030 |
0.002 |
5718.278 |
| DEMetro_Z |
6 |
10.228 |
0.032 |
0.002 |
4521.960 |
| DEMetro_Z |
8 |
9.968 |
0.034 |
0.003 |
3204.066 |
| DEMetro_Z |
10 |
9.686 |
0.036 |
0.005 |
1940.523 |
| DEMetro_Z |
12 |
9.816 |
0.038 |
0.006 |
1573.881 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
-1.909 |
0.062 |
-0.420 |
| HMC |
4 |
1.490 |
0.142 |
0.499 |
| HMC |
6 |
6.042 |
1.33e-06 |
12.294 |
| HMC |
8 |
6.374 |
5.69e-07 |
40.710 |
| HMC |
10 |
4.764 |
4.88e-05 |
34.451 |
| HMC |
12 |
5.603 |
4.74e-06 |
43.903 |
| SMC |
0 |
3.157 |
0.00253 |
0.835 |
| SMC |
4 |
3.303 |
0.00164 |
0.828 |
| SMC |
6 |
2.121 |
0.039 |
0.721 |
| SMC |
8 |
2.370 |
0.0215 |
0.738 |
| SMC |
10 |
0.231 |
0.818 |
0.060 |
| SMC |
12 |
1.269 |
0.21 |
0.427 |
| Metro |
0 |
16.248 |
3.3e-20 |
6.354 |
| Metro |
4 |
14.329 |
6.76e-18 |
5.858 |
| Metro |
6 |
7.730 |
1.15e-08 |
9.158 |
| Metro |
8 |
7.034 |
9.58e-08 |
29.655 |
| Metro |
10 |
6.726 |
2.2e-07 |
40.278 |
| Metro |
12 |
5.832 |
2.52e-06 |
42.680 |
| DEMetro_Z |
0 |
102.700 |
7.7e-39 |
405.945 |
| DEMetro_Z |
4 |
105.407 |
3.19e-39 |
351.379 |
| DEMetro_Z |
6 |
104.167 |
4.63e-39 |
359.313 |
| DEMetro_Z |
8 |
90.436 |
2.44e-37 |
265.789 |
| DEMetro_Z |
10 |
102.094 |
3.01e-39 |
187.793 |
| DEMetro_Z |
12 |
64.207 |
4.36e-33 |
160.511 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
100.983
|
1.7e-38
|
18.437
|
| DEMetro_Z_vs_SMC |
1
|
105.936
|
4.26e-39
|
19.341
|
| DEMetro_Z_vs_SMC |
2
|
101.463
|
1.48e-38
|
18.525
|
| DEMetro_Z_vs_SMC |
3
|
91.965
|
2.55e-37
|
16.790
|
| DEMetro_Z_vs_SMC |
4
|
100.604
|
1.9e-38
|
18.368
|
| DEMetro_Z_vs_SMC |
5
|
64.429
|
7.35e-33
|
11.763
|
| HMC_vs_Metro |
0
|
-20.372
|
9.96e-19
|
-3.719
|
| HMC_vs_Metro |
1
|
-12.770
|
1.97e-13
|
-2.332
|
| HMC_vs_Metro |
2
|
1.266
|
0.216
|
0.231
|
| HMC_vs_Metro |
3
|
1.441
|
0.16
|
0.263
|
| HMC_vs_Metro |
4
|
-0.836
|
0.41
|
-0.153
|
| HMC_vs_Metro |
5
|
0.278
|
0.783
|
0.051
|
| Metro_vs_DEMetro_Z |
0
|
-98.431
|
3.57e-38
|
-17.971
|
| Metro_vs_DEMetro_Z |
1
|
-105.716
|
4.53e-39
|
-19.301
|
| Metro_vs_DEMetro_Z |
2
|
-91.104
|
3.34e-37
|
-16.633
|
| Metro_vs_DEMetro_Z |
3
|
-42.951
|
8.33e-28
|
-7.842
|
| Metro_vs_DEMetro_Z |
4
|
-22.684
|
5.27e-20
|
-4.142
|
| Metro_vs_DEMetro_Z |
5
|
-16.842
|
1.63e-16
|
-3.075
|
| HMC_vs_SMC |
0
|
-6.480
|
4.31e-07
|
-1.183
|
| HMC_vs_SMC |
1
|
-1.060
|
0.298
|
-0.194
|
| HMC_vs_SMC |
2
|
5.653
|
4.14e-06
|
1.032
|
| HMC_vs_SMC |
3
|
6.231
|
8.47e-07
|
1.138
|
| HMC_vs_SMC |
4
|
4.778
|
4.7e-05
|
0.872
|
| HMC_vs_SMC |
5
|
5.560
|
5.36e-06
|
1.015
|
| Metro_vs_SMC |
0
|
15.968
|
6.62e-16
|
2.915
|
| Metro_vs_SMC |
1
|
12.221
|
5.81e-13
|
2.231
|
| Metro_vs_SMC |
2
|
7.411
|
3.64e-08
|
1.353
|
| Metro_vs_SMC |
3
|
6.909
|
1.36e-07
|
1.261
|
| Metro_vs_SMC |
4
|
6.779
|
1.93e-07
|
1.238
|
| Metro_vs_SMC |
5
|
5.792
|
2.82e-06
|
1.057
|
| HMC_vs_DEMetro_Z |
0
|
-100.832
|
1.78e-38
|
-18.409
|
| HMC_vs_DEMetro_Z |
1
|
-103.784
|
7.72e-39
|
-18.948
|
| HMC_vs_DEMetro_Z |
2
|
-86.464
|
1.51e-36
|
-15.786
|
| HMC_vs_DEMetro_Z |
3
|
-37.815
|
3.14e-26
|
-6.904
|
| HMC_vs_DEMetro_Z |
4
|
-22.327
|
8.15e-20
|
-4.076
|
| HMC_vs_DEMetro_Z |
5
|
-15.990
|
6.38e-16
|
-2.919
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.013 |
0.014 |
0.001 |
-0.420 |
| HMC |
4 |
0.015 |
0.014 |
0.002 |
0.499 |
| HMC |
6 |
0.033 |
0.014 |
0.002 |
12.294 |
| HMC |
8 |
0.099 |
0.014 |
0.002 |
40.710 |
| HMC |
10 |
0.118 |
0.014 |
0.003 |
34.451 |
| HMC |
12 |
0.167 |
0.014 |
0.003 |
43.903 |
| SMC |
0 |
0.015 |
0.014 |
0.001 |
0.835 |
| SMC |
4 |
0.015 |
0.014 |
0.002 |
0.828 |
| SMC |
6 |
0.015 |
0.014 |
0.002 |
0.721 |
| SMC |
8 |
0.015 |
0.014 |
0.002 |
0.738 |
| SMC |
10 |
0.014 |
0.014 |
0.003 |
0.060 |
| SMC |
12 |
0.015 |
0.014 |
0.003 |
0.427 |
| Metro |
0 |
0.023 |
0.014 |
0.001 |
6.354 |
| Metro |
4 |
0.023 |
0.014 |
0.002 |
5.858 |
| Metro |
6 |
0.028 |
0.014 |
0.002 |
9.158 |
| Metro |
8 |
0.076 |
0.014 |
0.002 |
29.655 |
| Metro |
10 |
0.135 |
0.014 |
0.003 |
40.278 |
| Metro |
12 |
0.163 |
0.014 |
0.003 |
42.680 |
| DEMetro_Z |
0 |
0.575 |
0.014 |
0.001 |
405.945 |
| DEMetro_Z |
4 |
0.577 |
0.014 |
0.002 |
351.379 |
| DEMetro_Z |
6 |
0.573 |
0.014 |
0.002 |
359.313 |
| DEMetro_Z |
8 |
0.573 |
0.014 |
0.002 |
265.789 |
| DEMetro_Z |
10 |
0.580 |
0.014 |
0.003 |
187.793 |
| DEMetro_Z |
12 |
0.574 |
0.014 |
0.003 |
160.511 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
-6.614 |
1.51e-08 |
-1.564 |
| HMC |
4 |
1.036 |
0.306 |
0.415 |
| HMC |
6 |
4.528 |
9.16e-05 |
10.174 |
| HMC |
8 |
8.829 |
1.02e-09 |
79.837 |
| HMC |
10 |
301.630 |
1.89e-78 |
109.318 |
| HMC |
12 |
272.613 |
3.58e-71 |
110.229 |
| SMC |
0 |
-0.281 |
0.78 |
-0.078 |
| SMC |
4 |
0.810 |
0.421 |
0.209 |
| SMC |
6 |
-0.246 |
0.807 |
-0.077 |
| SMC |
8 |
-0.128 |
0.899 |
-0.033 |
| SMC |
10 |
-1.406 |
0.166 |
-0.319 |
| SMC |
12 |
1.760 |
0.0843 |
0.556 |
| Metro |
0 |
13.730 |
9.27e-17 |
6.137 |
| Metro |
4 |
11.273 |
1.48e-13 |
5.797 |
| Metro |
6 |
5.857 |
2.15e-06 |
9.484 |
| Metro |
8 |
7.148 |
7.05e-08 |
27.490 |
| Metro |
10 |
8.180 |
5.05e-09 |
57.824 |
| Metro |
12 |
28.949 |
5e-23 |
105.026 |
| DEMetro_Z |
0 |
19.632 |
2.71e-18 |
4192.915 |
| DEMetro_Z |
4 |
23.277 |
2.59e-20 |
3401.720 |
| DEMetro_Z |
6 |
23.604 |
1.76e-20 |
3162.635 |
| DEMetro_Z |
8 |
22.480 |
6.75e-20 |
2204.379 |
| DEMetro_Z |
10 |
26.791 |
5.23e-22 |
1445.795 |
| DEMetro_Z |
12 |
27.692 |
2.07e-22 |
1102.424 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-19.641
|
2.68e-18
|
-3.586
|
| HMC_vs_DEMetro_Z |
1
|
-23.266
|
2.62e-20
|
-4.248
|
| HMC_vs_DEMetro_Z |
2
|
-23.481
|
2.04e-20
|
-4.287
|
| HMC_vs_DEMetro_Z |
3
|
-21.280
|
3.04e-19
|
-3.885
|
| HMC_vs_DEMetro_Z |
4
|
-24.804
|
4.47e-21
|
-4.529
|
| HMC_vs_DEMetro_Z |
5
|
-24.920
|
3.92e-21
|
-4.550
|
| Metro_vs_SMC |
0
|
15.299
|
2.02e-15
|
2.793
|
| Metro_vs_SMC |
1
|
10.816
|
1.08e-11
|
1.975
|
| Metro_vs_SMC |
2
|
6.162
|
1.02e-06
|
1.125
|
| Metro_vs_SMC |
3
|
7.174
|
6.75e-08
|
1.310
|
| Metro_vs_SMC |
4
|
8.206
|
4.77e-09
|
1.498
|
| Metro_vs_SMC |
5
|
28.919
|
6.16e-23
|
5.280
|
| Metro_vs_DEMetro_Z |
0
|
-19.610
|
2.8e-18
|
-3.580
|
| Metro_vs_DEMetro_Z |
1
|
-23.209
|
2.8e-20
|
-4.237
|
| Metro_vs_DEMetro_Z |
2
|
-23.659
|
1.65e-20
|
-4.320
|
| Metro_vs_DEMetro_Z |
3
|
-22.216
|
9.34e-20
|
-4.056
|
| Metro_vs_DEMetro_Z |
4
|
-25.739
|
1.6e-21
|
-4.699
|
| Metro_vs_DEMetro_Z |
5
|
-25.411
|
2.28e-21
|
-4.639
|
| HMC_vs_Metro |
0
|
-18.599
|
1.16e-17
|
-3.396
|
| HMC_vs_Metro |
1
|
-10.970
|
7.77e-12
|
-2.003
|
| HMC_vs_Metro |
2
|
0.246
|
0.808
|
0.045
|
| HMC_vs_Metro |
3
|
4.833
|
4.03e-05
|
0.882
|
| HMC_vs_Metro |
4
|
7.235
|
5.76e-08
|
1.321
|
| HMC_vs_Metro |
5
|
1.457
|
0.156
|
0.266
|
| HMC_vs_SMC |
0
|
-6.459
|
4.56e-07
|
-1.179
|
| HMC_vs_SMC |
1
|
0.530
|
0.6
|
0.097
|
| HMC_vs_SMC |
2
|
4.429
|
0.000124
|
0.809
|
| HMC_vs_SMC |
3
|
8.817
|
1.06e-09
|
1.610
|
| HMC_vs_SMC |
4
|
320.591
|
4.98e-53
|
58.532
|
| HMC_vs_SMC |
5
|
264.115
|
1.37e-50
|
48.221
|
| DEMetro_Z_vs_SMC |
0
|
19.633
|
2.71e-18
|
3.585
|
| DEMetro_Z_vs_SMC |
1
|
23.275
|
2.6e-20
|
4.249
|
| DEMetro_Z_vs_SMC |
2
|
23.611
|
1.75e-20
|
4.311
|
| DEMetro_Z_vs_SMC |
3
|
22.479
|
6.76e-20
|
4.104
|
| DEMetro_Z_vs_SMC |
4
|
26.793
|
5.22e-22
|
4.892
|
| DEMetro_Z_vs_SMC |
5
|
27.676
|
2.11e-22
|
5.053
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.018 |
0.022 |
0.002 |
-1.564 |
| HMC |
4 |
0.025 |
0.023 |
0.003 |
0.415 |
| HMC |
6 |
0.061 |
0.025 |
0.003 |
10.174 |
| HMC |
8 |
0.439 |
0.026 |
0.005 |
79.837 |
| HMC |
10 |
0.916 |
0.029 |
0.008 |
109.318 |
| HMC |
12 |
1.097 |
0.031 |
0.010 |
110.229 |
| SMC |
0 |
0.022 |
0.022 |
0.002 |
-0.078 |
| SMC |
4 |
0.024 |
0.023 |
0.003 |
0.209 |
| SMC |
6 |
0.025 |
0.025 |
0.003 |
-0.077 |
| SMC |
8 |
0.026 |
0.026 |
0.005 |
-0.033 |
| SMC |
10 |
0.026 |
0.029 |
0.008 |
-0.319 |
| SMC |
12 |
0.036 |
0.031 |
0.010 |
0.556 |
| Metro |
0 |
0.037 |
0.022 |
0.002 |
6.137 |
| Metro |
4 |
0.042 |
0.023 |
0.003 |
5.797 |
| Metro |
6 |
0.058 |
0.025 |
0.003 |
9.484 |
| Metro |
8 |
0.168 |
0.026 |
0.005 |
27.490 |
| Metro |
10 |
0.498 |
0.029 |
0.008 |
57.824 |
| Metro |
12 |
1.047 |
0.031 |
0.010 |
105.026 |
| DEMetro_Z |
0 |
10.067 |
0.022 |
0.002 |
4192.915 |
| DEMetro_Z |
4 |
11.105 |
0.023 |
0.003 |
3401.720 |
| DEMetro_Z |
6 |
11.017 |
0.025 |
0.003 |
3162.635 |
| DEMetro_Z |
8 |
11.425 |
0.026 |
0.005 |
2204.379 |
| DEMetro_Z |
10 |
11.755 |
0.029 |
0.008 |
1445.795 |
| DEMetro_Z |
12 |
10.698 |
0.031 |
0.010 |
1102.424 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
12.259 |
1.1e-17 |
3.319 |
| HMC |
4 |
6.219 |
7.2e-08 |
1.441 |
| HMC |
6 |
2.948 |
0.00536 |
1.363 |
| HMC |
8 |
6.607 |
3.05e-07 |
83.890 |
| HMC |
10 |
748.044 |
1.54e-83 |
344.374 |
| HMC |
12 |
939.064 |
7.39e-88 |
428.369 |
| SMC |
0 |
1.675 |
0.0993 |
0.403 |
| SMC |
4 |
-1.141 |
0.259 |
-0.257 |
| SMC |
6 |
0.084 |
0.933 |
0.021 |
| SMC |
8 |
-0.938 |
0.352 |
-0.235 |
| SMC |
10 |
1.079 |
0.286 |
0.351 |
| SMC |
12 |
2.315 |
0.0256 |
0.972 |
| Metro |
0 |
15.240 |
6.64e-20 |
5.414 |
| Metro |
4 |
8.970 |
1.17e-11 |
3.320 |
| Metro |
6 |
5.978 |
1.63e-07 |
1.699 |
| Metro |
8 |
3.498 |
0.00152 |
10.945 |
| Metro |
10 |
5.600 |
4.79e-06 |
139.606 |
| Metro |
12 |
22.826 |
4.41e-20 |
399.940 |
| DEMetro_Z |
0 |
17.535 |
5.61e-17 |
4605.416 |
| DEMetro_Z |
4 |
16.845 |
1.63e-16 |
3282.899 |
| DEMetro_Z |
6 |
14.818 |
4.6e-15 |
1674.091 |
| DEMetro_Z |
8 |
15.202 |
2.38e-15 |
1246.384 |
| DEMetro_Z |
10 |
16.238 |
4.27e-16 |
1613.106 |
| DEMetro_Z |
12 |
17.078 |
1.13e-16 |
1405.463 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
12.793
|
1.88e-13
|
2.336
|
| HMC_vs_SMC |
1
|
9.143
|
4.84e-10
|
1.669
|
| HMC_vs_SMC |
2
|
2.880
|
0.0074
|
0.526
|
| HMC_vs_SMC |
3
|
6.602
|
3.1e-07
|
1.205
|
| HMC_vs_SMC |
4
|
831.907
|
4.89e-65
|
151.885
|
| HMC_vs_SMC |
5
|
779.694
|
3.2e-64
|
142.352
|
| Metro_vs_DEMetro_Z |
0
|
-17.514
|
5.79e-17
|
-3.198
|
| Metro_vs_DEMetro_Z |
1
|
-16.821
|
1.69e-16
|
-3.071
|
| Metro_vs_DEMetro_Z |
2
|
-14.800
|
4.75e-15
|
-2.702
|
| Metro_vs_DEMetro_Z |
3
|
-15.106
|
2.8e-15
|
-2.758
|
| Metro_vs_DEMetro_Z |
4
|
-14.633
|
6.35e-15
|
-2.672
|
| Metro_vs_DEMetro_Z |
5
|
-11.758
|
1.48e-12
|
-2.147
|
| HMC_vs_Metro |
0
|
-5.684
|
3.81e-06
|
-1.038
|
| HMC_vs_Metro |
1
|
-5.644
|
4.25e-06
|
-1.030
|
| HMC_vs_Metro |
2
|
-0.710
|
0.483
|
-0.130
|
| HMC_vs_Metro |
3
|
5.368
|
9.11e-06
|
0.980
|
| HMC_vs_Metro |
4
|
8.200
|
4.85e-09
|
1.497
|
| HMC_vs_Metro |
5
|
1.602
|
0.12
|
0.292
|
| HMC_vs_DEMetro_Z |
0
|
-17.520
|
5.74e-17
|
-3.199
|
| HMC_vs_DEMetro_Z |
1
|
-16.840
|
1.64e-16
|
-3.074
|
| HMC_vs_DEMetro_Z |
2
|
-14.805
|
4.7e-15
|
-2.703
|
| HMC_vs_DEMetro_Z |
3
|
-14.102
|
1.63e-14
|
-2.575
|
| HMC_vs_DEMetro_Z |
4
|
-12.779
|
1.94e-13
|
-2.333
|
| HMC_vs_DEMetro_Z |
5
|
-11.871
|
1.18e-12
|
-2.167
|
| Metro_vs_SMC |
0
|
17.396
|
6.94e-17
|
3.176
|
| Metro_vs_SMC |
1
|
12.344
|
4.54e-13
|
2.254
|
| Metro_vs_SMC |
2
|
6.969
|
1.16e-07
|
1.272
|
| Metro_vs_SMC |
3
|
3.713
|
0.000868
|
0.678
|
| Metro_vs_SMC |
4
|
5.577
|
5.11e-06
|
1.018
|
| Metro_vs_SMC |
5
|
22.531
|
6.34e-20
|
4.114
|
| DEMetro_Z_vs_SMC |
0
|
17.531
|
5.64e-17
|
3.201
|
| DEMetro_Z_vs_SMC |
1
|
16.846
|
1.62e-16
|
3.076
|
| DEMetro_Z_vs_SMC |
2
|
14.810
|
4.66e-15
|
2.704
|
| DEMetro_Z_vs_SMC |
3
|
15.205
|
2.36e-15
|
2.776
|
| DEMetro_Z_vs_SMC |
4
|
16.241
|
4.25e-16
|
2.965
|
| DEMetro_Z_vs_SMC |
5
|
17.076
|
1.13e-16
|
3.118
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.045 |
0.032 |
0.004 |
3.319 |
| HMC |
4 |
0.046 |
0.036 |
0.007 |
1.441 |
| HMC |
6 |
0.058 |
0.041 |
0.013 |
1.363 |
| HMC |
8 |
1.447 |
0.045 |
0.017 |
83.890 |
| HMC |
10 |
4.565 |
0.046 |
0.013 |
344.374 |
| HMC |
12 |
6.569 |
0.044 |
0.015 |
428.369 |
| SMC |
0 |
0.033 |
0.032 |
0.004 |
0.403 |
| SMC |
4 |
0.034 |
0.036 |
0.007 |
-0.257 |
| SMC |
6 |
0.041 |
0.041 |
0.013 |
0.021 |
| SMC |
8 |
0.041 |
0.045 |
0.017 |
-0.235 |
| SMC |
10 |
0.051 |
0.046 |
0.013 |
0.351 |
| SMC |
12 |
0.058 |
0.044 |
0.015 |
0.972 |
| Metro |
0 |
0.054 |
0.032 |
0.004 |
5.414 |
| Metro |
4 |
0.058 |
0.036 |
0.007 |
3.320 |
| Metro |
6 |
0.063 |
0.041 |
0.013 |
1.699 |
| Metro |
8 |
0.228 |
0.045 |
0.017 |
10.945 |
| Metro |
10 |
1.878 |
0.046 |
0.013 |
139.606 |
| Metro |
12 |
6.136 |
0.044 |
0.015 |
399.940 |
| DEMetro_Z |
0 |
18.847 |
0.032 |
0.004 |
4605.416 |
| DEMetro_Z |
4 |
21.622 |
0.036 |
0.007 |
3282.899 |
| DEMetro_Z |
6 |
21.159 |
0.041 |
0.013 |
1674.091 |
| DEMetro_Z |
8 |
20.877 |
0.045 |
0.017 |
1246.384 |
| DEMetro_Z |
10 |
21.215 |
0.046 |
0.013 |
1613.106 |
| DEMetro_Z |
12 |
21.452 |
0.044 |
0.015 |
1405.463 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
0.370 |
0.713 |
0.079 |
| HMC |
4 |
3.407 |
0.00138 |
1.274 |
| HMC |
6 |
4.603 |
7.47e-05 |
11.445 |
| HMC |
8 |
8.624 |
1.69e-09 |
104.698 |
| HMC |
10 |
115.499 |
1.24e-41 |
142.538 |
| HMC |
12 |
113.785 |
1.54e-41 |
135.723 |
| SMC |
0 |
-0.146 |
0.885 |
-0.040 |
| SMC |
4 |
0.807 |
0.423 |
0.216 |
| SMC |
6 |
-0.007 |
0.994 |
-0.002 |
| SMC |
8 |
-0.065 |
0.948 |
-0.018 |
| SMC |
10 |
-1.428 |
0.159 |
-0.316 |
| SMC |
12 |
1.642 |
0.107 |
0.509 |
| Metro |
0 |
16.819 |
3.79e-20 |
7.135 |
| Metro |
4 |
12.959 |
6.87e-15 |
7.772 |
| Metro |
6 |
5.919 |
1.85e-06 |
10.924 |
| Metro |
8 |
6.719 |
2.23e-07 |
34.105 |
| Metro |
10 |
8.128 |
5.76e-09 |
73.104 |
| Metro |
12 |
27.023 |
3.74e-22 |
132.208 |
| DEMetro_Z |
0 |
20.728 |
6.21e-19 |
5642.196 |
| DEMetro_Z |
4 |
24.233 |
8.51e-21 |
5243.783 |
| DEMetro_Z |
6 |
26.110 |
1.07e-21 |
4050.163 |
| DEMetro_Z |
8 |
22.512 |
6.5e-20 |
3075.673 |
| DEMetro_Z |
10 |
27.157 |
3.58e-22 |
1960.126 |
| DEMetro_Z |
12 |
29.071 |
5.31e-23 |
1443.620 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-20.709
|
6.37e-19
|
-3.781
|
| Metro_vs_DEMetro_Z |
1
|
-24.176
|
9.09e-21
|
-4.414
|
| Metro_vs_DEMetro_Z |
2
|
-26.163
|
1.01e-21
|
-4.777
|
| Metro_vs_DEMetro_Z |
3
|
-22.272
|
8.72e-20
|
-4.066
|
| Metro_vs_DEMetro_Z |
4
|
-26.301
|
8.75e-22
|
-4.802
|
| Metro_vs_DEMetro_Z |
5
|
-26.774
|
5.33e-22
|
-4.888
|
| DEMetro_Z_vs_SMC |
0
|
20.725
|
6.24e-19
|
3.784
|
| DEMetro_Z_vs_SMC |
1
|
24.233
|
8.52e-21
|
4.424
|
| DEMetro_Z_vs_SMC |
2
|
26.119
|
1.06e-21
|
4.769
|
| DEMetro_Z_vs_SMC |
3
|
22.512
|
6.5e-20
|
4.110
|
| DEMetro_Z_vs_SMC |
4
|
27.163
|
3.56e-22
|
4.959
|
| DEMetro_Z_vs_SMC |
5
|
29.069
|
5.33e-23
|
5.307
|
| HMC_vs_DEMetro_Z |
0
|
-20.729
|
6.21e-19
|
-3.785
|
| HMC_vs_DEMetro_Z |
1
|
-24.222
|
8.62e-21
|
-4.422
|
| HMC_vs_DEMetro_Z |
2
|
-25.993
|
1.22e-21
|
-4.746
|
| HMC_vs_DEMetro_Z |
3
|
-21.397
|
2.61e-19
|
-3.906
|
| HMC_vs_DEMetro_Z |
4
|
-25.219
|
2.82e-21
|
-4.604
|
| HMC_vs_DEMetro_Z |
5
|
-26.223
|
9.51e-22
|
-4.788
|
| HMC_vs_Metro |
0
|
-18.407
|
1.54e-17
|
-3.361
|
| HMC_vs_Metro |
1
|
-11.754
|
1.5e-12
|
-2.146
|
| HMC_vs_Metro |
2
|
0.163
|
0.872
|
0.030
|
| HMC_vs_Metro |
3
|
4.922
|
3.15e-05
|
0.899
|
| HMC_vs_Metro |
4
|
7.366
|
4.09e-08
|
1.345
|
| HMC_vs_Metro |
5
|
0.723
|
0.475
|
0.132
|
| HMC_vs_SMC |
0
|
0.583
|
0.564
|
0.106
|
| HMC_vs_SMC |
1
|
2.719
|
0.0109
|
0.496
|
| HMC_vs_SMC |
2
|
4.492
|
0.000104
|
0.820
|
| HMC_vs_SMC |
3
|
8.606
|
1.77e-09
|
1.571
|
| HMC_vs_SMC |
4
|
119.802
|
1.21e-40
|
21.873
|
| HMC_vs_SMC |
5
|
113.120
|
6.39e-40
|
20.653
|
| Metro_vs_SMC |
0
|
18.591
|
1.18e-17
|
3.394
|
| Metro_vs_SMC |
1
|
12.447
|
3.71e-13
|
2.272
|
| Metro_vs_SMC |
2
|
6.150
|
1.06e-06
|
1.123
|
| Metro_vs_SMC |
3
|
6.738
|
2.15e-07
|
1.230
|
| Metro_vs_SMC |
4
|
8.153
|
5.46e-09
|
1.488
|
| Metro_vs_SMC |
5
|
27.006
|
4.19e-22
|
4.931
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.029 |
0.029 |
0.001 |
0.079 |
| HMC |
4 |
0.032 |
0.030 |
0.002 |
1.274 |
| HMC |
6 |
0.058 |
0.032 |
0.002 |
11.445 |
| HMC |
8 |
0.358 |
0.034 |
0.003 |
104.698 |
| HMC |
10 |
0.745 |
0.036 |
0.005 |
142.538 |
| HMC |
12 |
0.881 |
0.038 |
0.006 |
135.723 |
| SMC |
0 |
0.028 |
0.029 |
0.001 |
-0.040 |
| SMC |
4 |
0.030 |
0.030 |
0.002 |
0.216 |
| SMC |
6 |
0.032 |
0.032 |
0.002 |
-0.002 |
| SMC |
8 |
0.033 |
0.034 |
0.003 |
-0.018 |
| SMC |
10 |
0.035 |
0.036 |
0.005 |
-0.316 |
| SMC |
12 |
0.041 |
0.038 |
0.006 |
0.509 |
| Metro |
0 |
0.039 |
0.029 |
0.001 |
7.135 |
| Metro |
4 |
0.044 |
0.030 |
0.002 |
7.772 |
| Metro |
6 |
0.057 |
0.032 |
0.002 |
10.924 |
| Metro |
8 |
0.139 |
0.034 |
0.003 |
34.105 |
| Metro |
10 |
0.400 |
0.036 |
0.005 |
73.104 |
| Metro |
12 |
0.860 |
0.038 |
0.006 |
132.208 |
| DEMetro_Z |
0 |
8.463 |
0.029 |
0.001 |
5642.196 |
| DEMetro_Z |
4 |
9.304 |
0.030 |
0.002 |
5243.783 |
| DEMetro_Z |
6 |
9.164 |
0.032 |
0.002 |
4050.163 |
| DEMetro_Z |
8 |
9.570 |
0.034 |
0.003 |
3075.673 |
| DEMetro_Z |
10 |
9.783 |
0.036 |
0.005 |
1960.126 |
| DEMetro_Z |
12 |
9.007 |
0.038 |
0.006 |
1443.620 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
-1.164 |
0.25 |
-0.261 |
| HMC |
4 |
2.686 |
0.01 |
0.982 |
| HMC |
6 |
4.624 |
7.02e-05 |
10.965 |
| HMC |
8 |
8.726 |
1.31e-09 |
90.777 |
| HMC |
10 |
141.163 |
1.3e-45 |
128.604 |
| HMC |
12 |
148.294 |
1.01e-46 |
126.378 |
| SMC |
0 |
0.633 |
0.529 |
0.165 |
| SMC |
4 |
0.992 |
0.326 |
0.259 |
| SMC |
6 |
0.172 |
0.864 |
0.053 |
| SMC |
8 |
-0.349 |
0.728 |
-0.091 |
| SMC |
10 |
-0.934 |
0.355 |
-0.212 |
| SMC |
12 |
1.811 |
0.0758 |
0.561 |
| Metro |
0 |
13.728 |
6.87e-17 |
5.980 |
| Metro |
4 |
12.361 |
7.09e-15 |
6.111 |
| Metro |
6 |
6.086 |
1.14e-06 |
10.262 |
| Metro |
8 |
7.022 |
9.9e-08 |
30.401 |
| Metro |
10 |
7.944 |
9.18e-09 |
67.634 |
| Metro |
12 |
28.439 |
8.64e-23 |
120.605 |
| DEMetro_Z |
0 |
86.839 |
1.24e-36 |
657.813 |
| DEMetro_Z |
4 |
78.852 |
2e-35 |
576.318 |
| DEMetro_Z |
6 |
118.626 |
1.31e-40 |
579.008 |
| DEMetro_Z |
8 |
68.206 |
1.29e-33 |
438.999 |
| DEMetro_Z |
10 |
61.773 |
2.13e-32 |
311.241 |
| DEMetro_Z |
12 |
61.765 |
2.01e-32 |
264.209 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
86.939
|
1.29e-36
|
15.873
|
| DEMetro_Z_vs_SMC |
1
|
79.083
|
1.99e-35
|
14.439
|
| DEMetro_Z_vs_SMC |
2
|
118.347
|
1.73e-40
|
21.607
|
| DEMetro_Z_vs_SMC |
3
|
68.173
|
1.44e-33
|
12.447
|
| DEMetro_Z_vs_SMC |
4
|
61.861
|
2.37e-32
|
11.294
|
| DEMetro_Z_vs_SMC |
5
|
61.133
|
3.33e-32
|
11.161
|
| HMC_vs_Metro |
0
|
-16.280
|
3.99e-16
|
-2.972
|
| HMC_vs_Metro |
1
|
-10.659
|
1.52e-11
|
-1.946
|
| HMC_vs_Metro |
2
|
0.235
|
0.816
|
0.043
|
| HMC_vs_Metro |
3
|
4.877
|
3.57e-05
|
0.890
|
| HMC_vs_Metro |
4
|
7.241
|
5.66e-08
|
1.322
|
| HMC_vs_Metro |
5
|
1.318
|
0.198
|
0.241
|
| Metro_vs_DEMetro_Z |
0
|
-87.236
|
1.17e-36
|
-15.927
|
| Metro_vs_DEMetro_Z |
1
|
-76.438
|
5.32e-35
|
-13.956
|
| Metro_vs_DEMetro_Z |
2
|
-113.312
|
6.08e-40
|
-20.688
|
| Metro_vs_DEMetro_Z |
3
|
-58.453
|
1.21e-31
|
-10.672
|
| Metro_vs_DEMetro_Z |
4
|
-22.403
|
7.42e-20
|
-4.090
|
| Metro_vs_DEMetro_Z |
5
|
-22.485
|
6.71e-20
|
-4.105
|
| HMC_vs_SMC |
0
|
-2.265
|
0.0312
|
-0.413
|
| HMC_vs_SMC |
1
|
2.102
|
0.0444
|
0.384
|
| HMC_vs_SMC |
2
|
4.515
|
9.73e-05
|
0.824
|
| HMC_vs_SMC |
3
|
8.722
|
1.33e-09
|
1.592
|
| HMC_vs_SMC |
4
|
142.599
|
7.83e-43
|
26.035
|
| HMC_vs_SMC |
5
|
147.735
|
2.81e-43
|
26.973
|
| Metro_vs_SMC |
0
|
14.992
|
3.41e-15
|
2.737
|
| Metro_vs_SMC |
1
|
11.726
|
1.58e-12
|
2.141
|
| Metro_vs_SMC |
2
|
6.348
|
6.16e-07
|
1.159
|
| Metro_vs_SMC |
3
|
7.070
|
8.88e-08
|
1.291
|
| Metro_vs_SMC |
4
|
7.956
|
8.95e-09
|
1.453
|
| Metro_vs_SMC |
5
|
28.400
|
1.02e-22
|
5.185
|
| HMC_vs_DEMetro_Z |
0
|
-86.965
|
1.28e-36
|
-15.878
|
| HMC_vs_DEMetro_Z |
1
|
-79.576
|
1.66e-35
|
-14.529
|
| HMC_vs_DEMetro_Z |
2
|
-95.742
|
7.95e-38
|
-17.480
|
| HMC_vs_DEMetro_Z |
3
|
-29.515
|
3.47e-23
|
-5.389
|
| HMC_vs_DEMetro_Z |
4
|
-36.484
|
8.7e-26
|
-6.661
|
| HMC_vs_DEMetro_Z |
5
|
-32.062
|
3.38e-24
|
-5.854
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.013 |
0.014 |
0.001 |
-0.261 |
| HMC |
4 |
0.015 |
0.014 |
0.002 |
0.982 |
| HMC |
6 |
0.031 |
0.014 |
0.002 |
10.965 |
| HMC |
8 |
0.205 |
0.014 |
0.002 |
90.777 |
| HMC |
10 |
0.402 |
0.014 |
0.003 |
128.604 |
| HMC |
12 |
0.455 |
0.014 |
0.003 |
126.378 |
| SMC |
0 |
0.014 |
0.014 |
0.001 |
0.165 |
| SMC |
4 |
0.014 |
0.014 |
0.002 |
0.259 |
| SMC |
6 |
0.014 |
0.014 |
0.002 |
0.053 |
| SMC |
8 |
0.013 |
0.014 |
0.002 |
-0.091 |
| SMC |
10 |
0.013 |
0.014 |
0.003 |
-0.212 |
| SMC |
12 |
0.016 |
0.014 |
0.003 |
0.561 |
| Metro |
0 |
0.022 |
0.014 |
0.001 |
5.980 |
| Metro |
4 |
0.024 |
0.014 |
0.002 |
6.111 |
| Metro |
6 |
0.030 |
0.014 |
0.002 |
10.262 |
| Metro |
8 |
0.078 |
0.014 |
0.002 |
30.401 |
| Metro |
10 |
0.218 |
0.014 |
0.003 |
67.634 |
| Metro |
12 |
0.435 |
0.014 |
0.003 |
120.605 |
| DEMetro_Z |
0 |
0.923 |
0.014 |
0.001 |
657.813 |
| DEMetro_Z |
4 |
0.938 |
0.014 |
0.002 |
576.318 |
| DEMetro_Z |
6 |
0.915 |
0.014 |
0.002 |
579.008 |
| DEMetro_Z |
8 |
0.938 |
0.014 |
0.002 |
438.999 |
| DEMetro_Z |
10 |
0.952 |
0.014 |
0.003 |
311.241 |
| DEMetro_Z |
12 |
0.936 |
0.014 |
0.003 |
264.209 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_high_Correlation
(Mixture,
mm,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
1.568 |
0.123 |
0.523 |
| HMC |
4 |
2.150 |
0.0369 |
0.806 |
| HMC |
6 |
5.682 |
3.38e-06 |
7.823 |
| HMC |
8 |
7.097 |
7.92e-08 |
20.652 |
| HMC |
10 |
5.970 |
1.68e-06 |
18.449 |
| HMC |
12 |
5.286 |
1.13e-05 |
21.701 |
| SMC |
0 |
-0.950 |
0.346 |
-0.222 |
| SMC |
4 |
-0.541 |
0.591 |
-0.141 |
| SMC |
6 |
1.750 |
0.0872 |
0.683 |
| SMC |
8 |
0.040 |
0.968 |
0.011 |
| SMC |
10 |
-0.555 |
0.581 |
-0.132 |
| SMC |
12 |
-0.301 |
0.764 |
-0.078 |
| Metro |
0 |
5.536 |
4.7e-06 |
5.780 |
| Metro |
4 |
7.365 |
1.58e-08 |
4.799 |
| Metro |
6 |
5.417 |
6.57e-06 |
5.576 |
| Metro |
8 |
6.713 |
1.83e-07 |
8.215 |
| Metro |
10 |
9.396 |
1.53e-10 |
10.180 |
| Metro |
12 |
9.108 |
4.73e-10 |
21.980 |
| DEMetro_Z |
0 |
3.404 |
0.00136 |
1.207 |
| DEMetro_Z |
4 |
2.433 |
0.0191 |
0.945 |
| DEMetro_Z |
6 |
5.745 |
2.18e-06 |
4.453 |
| DEMetro_Z |
8 |
4.860 |
3.61e-05 |
10.340 |
| DEMetro_Z |
10 |
8.552 |
1.78e-09 |
17.778 |
| DEMetro_Z |
12 |
6.677 |
2.47e-07 |
24.053 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.627
|
0.115
|
-0.297
|
| HMC_vs_DEMetro_Z |
1
|
-0.306
|
0.762
|
-0.056
|
| HMC_vs_DEMetro_Z |
2
|
2.255
|
0.0319
|
0.412
|
| HMC_vs_DEMetro_Z |
3
|
2.789
|
0.00923
|
0.509
|
| HMC_vs_DEMetro_Z |
4
|
0.173
|
0.864
|
0.032
|
| HMC_vs_DEMetro_Z |
5
|
-0.554
|
0.584
|
-0.101
|
| Metro_vs_SMC |
0
|
6.021
|
1.51e-06
|
1.099
|
| Metro_vs_SMC |
1
|
7.054
|
9.28e-08
|
1.288
|
| Metro_vs_SMC |
2
|
4.563
|
8.53e-05
|
0.833
|
| Metro_vs_SMC |
3
|
6.661
|
2.65e-07
|
1.216
|
| Metro_vs_SMC |
4
|
9.069
|
5.78e-10
|
1.656
|
| Metro_vs_SMC |
5
|
9.013
|
6.6e-10
|
1.646
|
| Metro_vs_DEMetro_Z |
0
|
4.570
|
8.37e-05
|
0.834
|
| Metro_vs_DEMetro_Z |
1
|
5.864
|
2.32e-06
|
1.071
|
| Metro_vs_DEMetro_Z |
2
|
0.923
|
0.364
|
0.168
|
| Metro_vs_DEMetro_Z |
3
|
-0.896
|
0.378
|
-0.164
|
| Metro_vs_DEMetro_Z |
4
|
-3.153
|
0.00374
|
-0.576
|
| Metro_vs_DEMetro_Z |
5
|
-0.440
|
0.663
|
-0.080
|
| HMC_vs_Metro |
0
|
-4.942
|
2.98e-05
|
-0.902
|
| HMC_vs_Metro |
1
|
-5.812
|
2.67e-06
|
-1.061
|
| HMC_vs_Metro |
2
|
1.160
|
0.255
|
0.212
|
| HMC_vs_Metro |
3
|
3.785
|
0.000714
|
0.691
|
| HMC_vs_Metro |
4
|
2.373
|
0.0245
|
0.433
|
| HMC_vs_Metro |
5
|
-0.052
|
0.959
|
-0.009
|
| HMC_vs_SMC |
0
|
2.493
|
0.0186
|
0.455
|
| HMC_vs_SMC |
1
|
2.414
|
0.0223
|
0.441
|
| HMC_vs_SMC |
2
|
5.235
|
1.32e-05
|
0.956
|
| HMC_vs_SMC |
3
|
7.203
|
6.26e-08
|
1.315
|
| HMC_vs_SMC |
4
|
6.053
|
1.38e-06
|
1.105
|
| HMC_vs_SMC |
5
|
5.280
|
1.16e-05
|
0.964
|
| DEMetro_Z_vs_SMC |
0
|
4.044
|
0.000355
|
0.738
|
| DEMetro_Z_vs_SMC |
1
|
2.830
|
0.00836
|
0.517
|
| DEMetro_Z_vs_SMC |
2
|
4.527
|
9.41e-05
|
0.827
|
| DEMetro_Z_vs_SMC |
3
|
4.780
|
4.67e-05
|
0.873
|
| DEMetro_Z_vs_SMC |
4
|
8.617
|
1.72e-09
|
1.573
|
| DEMetro_Z_vs_SMC |
5
|
6.656
|
2.68e-07
|
1.215
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.032 |
0.023 |
0.016 |
0.523 |
| HMC |
4 |
0.032 |
0.022 |
0.013 |
0.806 |
| HMC |
6 |
0.106 |
0.020 |
0.011 |
7.823 |
| HMC |
8 |
0.347 |
0.026 |
0.016 |
20.652 |
| HMC |
10 |
0.393 |
0.026 |
0.020 |
18.449 |
| HMC |
12 |
0.418 |
0.030 |
0.018 |
21.701 |
| SMC |
0 |
0.020 |
0.023 |
0.016 |
-0.222 |
| SMC |
4 |
0.020 |
0.022 |
0.013 |
-0.141 |
| SMC |
6 |
0.027 |
0.020 |
0.011 |
0.683 |
| SMC |
8 |
0.026 |
0.026 |
0.016 |
0.011 |
| SMC |
10 |
0.024 |
0.026 |
0.020 |
-0.132 |
| SMC |
12 |
0.028 |
0.030 |
0.018 |
-0.078 |
| Metro |
0 |
0.114 |
0.023 |
0.016 |
5.780 |
| Metro |
4 |
0.083 |
0.022 |
0.013 |
4.799 |
| Metro |
6 |
0.082 |
0.020 |
0.011 |
5.576 |
| Metro |
8 |
0.154 |
0.026 |
0.016 |
8.215 |
| Metro |
10 |
0.229 |
0.026 |
0.020 |
10.180 |
| Metro |
12 |
0.423 |
0.030 |
0.018 |
21.980 |
| DEMetro_Z |
0 |
0.042 |
0.023 |
0.016 |
1.207 |
| DEMetro_Z |
4 |
0.034 |
0.022 |
0.013 |
0.945 |
| DEMetro_Z |
6 |
0.069 |
0.020 |
0.011 |
4.453 |
| DEMetro_Z |
8 |
0.187 |
0.026 |
0.016 |
10.340 |
| DEMetro_Z |
10 |
0.379 |
0.026 |
0.020 |
17.778 |
| DEMetro_Z |
12 |
0.461 |
0.030 |
0.018 |
24.053 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
2.156 |
0.0372 |
1.000 |
| HMC |
4 |
4.702 |
2.87e-05 |
2.010 |
| HMC |
6 |
2.732 |
0.0087 |
0.915 |
| HMC |
8 |
4.643 |
6.43e-05 |
6.967 |
| HMC |
10 |
4.251 |
0.000198 |
9.985 |
| HMC |
12 |
3.890 |
0.000532 |
9.991 |
| SMC |
0 |
-2.572 |
0.0129 |
-0.587 |
| SMC |
4 |
1.153 |
0.254 |
0.349 |
| SMC |
6 |
-0.748 |
0.457 |
-0.213 |
| SMC |
8 |
-0.390 |
0.698 |
-0.092 |
| SMC |
10 |
1.364 |
0.178 |
0.381 |
| SMC |
12 |
-1.022 |
0.311 |
-0.239 |
| Metro |
0 |
7.268 |
3.91e-08 |
8.366 |
| Metro |
4 |
6.431 |
1.78e-07 |
3.478 |
| Metro |
6 |
5.427 |
5.37e-06 |
4.030 |
| Metro |
8 |
7.190 |
2.52e-08 |
4.588 |
| Metro |
10 |
6.801 |
1.24e-07 |
6.452 |
| Metro |
12 |
6.782 |
1.65e-07 |
10.360 |
| DEMetro_Z |
0 |
3.734 |
0.000525 |
1.407 |
| DEMetro_Z |
4 |
4.031 |
0.000217 |
1.573 |
| DEMetro_Z |
6 |
4.563 |
4.38e-05 |
1.921 |
| DEMetro_Z |
8 |
2.527 |
0.017 |
3.316 |
| DEMetro_Z |
10 |
6.212 |
7.09e-07 |
6.881 |
| DEMetro_Z |
12 |
4.467 |
0.000108 |
9.383 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.400
|
0.00198
|
0.621
|
| HMC_vs_SMC |
1
|
3.877
|
0.000558
|
0.708
|
| HMC_vs_SMC |
2
|
3.515
|
0.00147
|
0.642
|
| HMC_vs_SMC |
3
|
4.617
|
7.35e-05
|
0.843
|
| HMC_vs_SMC |
4
|
4.124
|
0.000285
|
0.753
|
| HMC_vs_SMC |
5
|
4.024
|
0.000375
|
0.735
|
| Metro_vs_DEMetro_Z |
0
|
6.037
|
1.44e-06
|
1.102
|
| Metro_vs_DEMetro_Z |
1
|
3.314
|
0.00248
|
0.605
|
| Metro_vs_DEMetro_Z |
2
|
2.477
|
0.0193
|
0.452
|
| Metro_vs_DEMetro_Z |
3
|
0.840
|
0.408
|
0.153
|
| Metro_vs_DEMetro_Z |
4
|
-0.297
|
0.769
|
-0.054
|
| Metro_vs_DEMetro_Z |
5
|
0.360
|
0.722
|
0.066
|
| HMC_vs_Metro |
0
|
-5.770
|
3e-06
|
-1.053
|
| HMC_vs_Metro |
1
|
-2.512
|
0.0178
|
-0.459
|
| HMC_vs_Metro |
2
|
-4.567
|
8.44e-05
|
-0.834
|
| HMC_vs_Metro |
3
|
1.547
|
0.133
|
0.282
|
| HMC_vs_Metro |
4
|
1.344
|
0.189
|
0.245
|
| HMC_vs_Metro |
5
|
-0.121
|
0.905
|
-0.022
|
| HMC_vs_DEMetro_Z |
0
|
-0.726
|
0.473
|
-0.133
|
| HMC_vs_DEMetro_Z |
1
|
0.864
|
0.395
|
0.158
|
| HMC_vs_DEMetro_Z |
2
|
-1.983
|
0.0569
|
-0.362
|
| HMC_vs_DEMetro_Z |
3
|
1.684
|
0.103
|
0.307
|
| HMC_vs_DEMetro_Z |
4
|
1.265
|
0.216
|
0.231
|
| HMC_vs_DEMetro_Z |
5
|
0.191
|
0.85
|
0.035
|
| Metro_vs_SMC |
0
|
7.696
|
1.74e-08
|
1.405
|
| Metro_vs_SMC |
1
|
5.119
|
1.82e-05
|
0.935
|
| Metro_vs_SMC |
2
|
5.850
|
2.41e-06
|
1.068
|
| Metro_vs_SMC |
3
|
7.456
|
3.23e-08
|
1.361
|
| Metro_vs_SMC |
4
|
6.374
|
5.75e-07
|
1.164
|
| Metro_vs_SMC |
5
|
6.888
|
1.44e-07
|
1.258
|
| DEMetro_Z_vs_SMC |
0
|
5.394
|
8.49e-06
|
0.985
|
| DEMetro_Z_vs_SMC |
1
|
3.390
|
0.00203
|
0.619
|
| DEMetro_Z_vs_SMC |
2
|
5.163
|
1.61e-05
|
0.943
|
| DEMetro_Z_vs_SMC |
3
|
2.565
|
0.0158
|
0.468
|
| DEMetro_Z_vs_SMC |
4
|
6.077
|
1.29e-06
|
1.110
|
| DEMetro_Z_vs_SMC |
5
|
4.615
|
7.39e-05
|
0.843
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.044 |
0.028 |
0.016 |
1.000 |
| HMC |
4 |
0.064 |
0.029 |
0.017 |
2.010 |
| HMC |
6 |
0.064 |
0.044 |
0.022 |
0.915 |
| HMC |
8 |
0.249 |
0.047 |
0.029 |
6.967 |
| HMC |
10 |
0.414 |
0.054 |
0.036 |
9.985 |
| HMC |
12 |
0.484 |
0.065 |
0.042 |
9.991 |
| SMC |
0 |
0.019 |
0.028 |
0.016 |
-0.587 |
| SMC |
4 |
0.035 |
0.029 |
0.017 |
0.349 |
| SMC |
6 |
0.039 |
0.044 |
0.022 |
-0.213 |
| SMC |
8 |
0.044 |
0.047 |
0.029 |
-0.092 |
| SMC |
10 |
0.067 |
0.054 |
0.036 |
0.381 |
| SMC |
12 |
0.055 |
0.065 |
0.042 |
-0.239 |
| Metro |
0 |
0.160 |
0.028 |
0.016 |
8.366 |
| Metro |
4 |
0.090 |
0.029 |
0.017 |
3.478 |
| Metro |
6 |
0.134 |
0.044 |
0.022 |
4.030 |
| Metro |
8 |
0.180 |
0.047 |
0.029 |
4.588 |
| Metro |
10 |
0.287 |
0.054 |
0.036 |
6.452 |
| Metro |
12 |
0.499 |
0.065 |
0.042 |
10.360 |
| DEMetro_Z |
0 |
0.050 |
0.028 |
0.016 |
1.407 |
| DEMetro_Z |
4 |
0.057 |
0.029 |
0.017 |
1.573 |
| DEMetro_Z |
6 |
0.087 |
0.044 |
0.022 |
1.921 |
| DEMetro_Z |
8 |
0.143 |
0.047 |
0.029 |
3.316 |
| DEMetro_Z |
10 |
0.302 |
0.054 |
0.036 |
6.881 |
| DEMetro_Z |
12 |
0.458 |
0.065 |
0.042 |
9.383 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
2.915 |
0.00532 |
0.979 |
| HMC |
4 |
4.854 |
1.79e-05 |
2.098 |
| HMC |
6 |
6.015 |
1.42e-06 |
11.279 |
| HMC |
8 |
6.979 |
1.1e-07 |
25.887 |
| HMC |
10 |
5.806 |
2.68e-06 |
25.060 |
| HMC |
12 |
5.433 |
7.56e-06 |
26.258 |
| SMC |
0 |
-1.588 |
0.118 |
-0.355 |
| SMC |
4 |
-0.553 |
0.583 |
-0.156 |
| SMC |
6 |
2.353 |
0.0235 |
1.026 |
| SMC |
8 |
-0.326 |
0.746 |
-0.083 |
| SMC |
10 |
0.157 |
0.875 |
0.040 |
| SMC |
12 |
-1.290 |
0.202 |
-0.320 |
| Metro |
0 |
7.325 |
3.39e-08 |
8.602 |
| Metro |
4 |
10.799 |
2.51e-12 |
7.985 |
| Metro |
6 |
8.180 |
3.45e-09 |
9.315 |
| Metro |
8 |
8.254 |
3.26e-09 |
11.583 |
| Metro |
10 |
11.065 |
4.3e-12 |
16.327 |
| Metro |
12 |
9.477 |
2.03e-10 |
27.583 |
| DEMetro_Z |
0 |
5.847 |
4.32e-07 |
2.054 |
| DEMetro_Z |
4 |
7.227 |
8.22e-09 |
3.162 |
| DEMetro_Z |
6 |
9.223 |
1.5e-10 |
7.376 |
| DEMetro_Z |
8 |
5.182 |
1.48e-05 |
12.971 |
| DEMetro_Z |
10 |
8.553 |
1.89e-09 |
25.263 |
| DEMetro_Z |
12 |
7.009 |
1.02e-07 |
29.212 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
5.825
|
2.58e-06
|
1.063
|
| Metro_vs_DEMetro_Z |
1
|
6.428
|
4.96e-07
|
1.174
|
| Metro_vs_DEMetro_Z |
2
|
1.424
|
0.165
|
0.260
|
| Metro_vs_DEMetro_Z |
3
|
-0.503
|
0.619
|
-0.092
|
| Metro_vs_DEMetro_Z |
4
|
-2.562
|
0.0159
|
-0.468
|
| Metro_vs_DEMetro_Z |
5
|
-0.299
|
0.767
|
-0.055
|
| DEMetro_Z_vs_SMC |
0
|
7.218
|
6.02e-08
|
1.318
|
| DEMetro_Z_vs_SMC |
1
|
6.925
|
1.31e-07
|
1.264
|
| DEMetro_Z_vs_SMC |
2
|
7.255
|
5.46e-08
|
1.325
|
| DEMetro_Z_vs_SMC |
3
|
5.167
|
1.6e-05
|
0.943
|
| DEMetro_Z_vs_SMC |
4
|
8.560
|
1.98e-09
|
1.563
|
| DEMetro_Z_vs_SMC |
5
|
7.087
|
8.49e-08
|
1.294
|
| HMC_vs_DEMetro_Z |
0
|
-2.531
|
0.017
|
-0.462
|
| HMC_vs_DEMetro_Z |
1
|
-1.867
|
0.0721
|
-0.341
|
| HMC_vs_DEMetro_Z |
2
|
1.985
|
0.0566
|
0.362
|
| HMC_vs_DEMetro_Z |
3
|
2.778
|
0.0095
|
0.507
|
| HMC_vs_DEMetro_Z |
4
|
-0.037
|
0.97
|
-0.007
|
| HMC_vs_DEMetro_Z |
5
|
-0.622
|
0.539
|
-0.114
|
| HMC_vs_Metro |
0
|
-6.373
|
5.76e-07
|
-1.164
|
| HMC_vs_Metro |
1
|
-8.568
|
1.94e-09
|
-1.564
|
| HMC_vs_Metro |
2
|
0.781
|
0.441
|
0.143
|
| HMC_vs_Metro |
3
|
3.503
|
0.00151
|
0.640
|
| HMC_vs_Metro |
4
|
1.795
|
0.083
|
0.328
|
| HMC_vs_Metro |
5
|
-0.210
|
0.835
|
-0.038
|
| HMC_vs_SMC |
0
|
4.180
|
0.000245
|
0.763
|
| HMC_vs_SMC |
1
|
4.644
|
6.81e-05
|
0.848
|
| HMC_vs_SMC |
2
|
5.515
|
6.07e-06
|
1.007
|
| HMC_vs_SMC |
3
|
7.043
|
9.54e-08
|
1.286
|
| HMC_vs_SMC |
4
|
5.827
|
2.56e-06
|
1.064
|
| HMC_vs_SMC |
5
|
5.509
|
6.17e-06
|
1.006
|
| Metro_vs_SMC |
0
|
7.830
|
1.23e-08
|
1.430
|
| Metro_vs_SMC |
1
|
10.082
|
5.49e-11
|
1.841
|
| Metro_vs_SMC |
2
|
6.878
|
1.48e-07
|
1.256
|
| Metro_vs_SMC |
3
|
8.241
|
4.37e-09
|
1.505
|
| Metro_vs_SMC |
4
|
10.662
|
1.51e-11
|
1.947
|
| Metro_vs_SMC |
5
|
9.476
|
2.21e-10
|
1.730
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.041 |
0.030 |
0.011 |
0.979 |
| HMC |
4 |
0.046 |
0.030 |
0.008 |
2.098 |
| HMC |
6 |
0.108 |
0.031 |
0.007 |
11.279 |
| HMC |
8 |
0.317 |
0.036 |
0.011 |
25.887 |
| HMC |
10 |
0.357 |
0.036 |
0.013 |
25.060 |
| HMC |
12 |
0.387 |
0.043 |
0.013 |
26.258 |
| SMC |
0 |
0.026 |
0.030 |
0.011 |
-0.355 |
| SMC |
4 |
0.029 |
0.030 |
0.008 |
-0.156 |
| SMC |
6 |
0.038 |
0.031 |
0.007 |
1.026 |
| SMC |
8 |
0.036 |
0.036 |
0.011 |
-0.083 |
| SMC |
10 |
0.037 |
0.036 |
0.013 |
0.040 |
| SMC |
12 |
0.039 |
0.043 |
0.013 |
-0.320 |
| Metro |
0 |
0.125 |
0.030 |
0.011 |
8.602 |
| Metro |
4 |
0.090 |
0.030 |
0.008 |
7.985 |
| Metro |
6 |
0.095 |
0.031 |
0.007 |
9.315 |
| Metro |
8 |
0.162 |
0.036 |
0.011 |
11.583 |
| Metro |
10 |
0.245 |
0.036 |
0.013 |
16.327 |
| Metro |
12 |
0.404 |
0.043 |
0.013 |
27.583 |
| DEMetro_Z |
0 |
0.053 |
0.030 |
0.011 |
2.054 |
| DEMetro_Z |
4 |
0.054 |
0.030 |
0.008 |
3.162 |
| DEMetro_Z |
6 |
0.081 |
0.031 |
0.007 |
7.376 |
| DEMetro_Z |
8 |
0.177 |
0.036 |
0.011 |
12.971 |
| DEMetro_Z |
10 |
0.359 |
0.036 |
0.013 |
25.263 |
| DEMetro_Z |
12 |
0.426 |
0.043 |
0.013 |
29.212 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
2.219 |
0.0307 |
0.677 |
| HMC |
4 |
4.999 |
8.87e-06 |
1.853 |
| HMC |
6 |
5.863 |
2.07e-06 |
8.687 |
| HMC |
8 |
7.136 |
7.21e-08 |
23.751 |
| HMC |
10 |
5.889 |
2.12e-06 |
21.933 |
| HMC |
12 |
5.161 |
1.61e-05 |
23.065 |
| SMC |
0 |
-1.302 |
0.199 |
-0.292 |
| SMC |
4 |
-0.481 |
0.633 |
-0.114 |
| SMC |
6 |
1.922 |
0.0607 |
0.681 |
| SMC |
8 |
-0.650 |
0.518 |
-0.158 |
| SMC |
10 |
-0.227 |
0.821 |
-0.054 |
| SMC |
12 |
-1.061 |
0.293 |
-0.261 |
| Metro |
0 |
7.392 |
2.52e-08 |
7.347 |
| Metro |
4 |
10.883 |
6.63e-13 |
6.095 |
| Metro |
6 |
9.669 |
3.34e-11 |
6.659 |
| Metro |
8 |
8.653 |
9.27e-10 |
8.893 |
| Metro |
10 |
12.644 |
9.15e-14 |
12.749 |
| Metro |
12 |
9.606 |
1.46e-10 |
23.589 |
| DEMetro_Z |
0 |
4.930 |
8.91e-06 |
1.579 |
| DEMetro_Z |
4 |
6.369 |
9.93e-08 |
2.514 |
| DEMetro_Z |
6 |
8.143 |
1.83e-09 |
5.440 |
| DEMetro_Z |
8 |
4.792 |
4.42e-05 |
12.093 |
| DEMetro_Z |
10 |
8.818 |
9.55e-10 |
21.070 |
| DEMetro_Z |
12 |
6.686 |
2.41e-07 |
25.739 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
6.174
|
9.91e-07
|
1.127
|
| DEMetro_Z_vs_SMC |
1
|
6.746
|
2.1e-07
|
1.232
|
| DEMetro_Z_vs_SMC |
2
|
6.819
|
1.73e-07
|
1.245
|
| DEMetro_Z_vs_SMC |
3
|
4.824
|
4.14e-05
|
0.881
|
| DEMetro_Z_vs_SMC |
4
|
8.871
|
9.3e-10
|
1.620
|
| DEMetro_Z_vs_SMC |
5
|
6.757
|
2.05e-07
|
1.234
|
| HMC_vs_Metro |
0
|
-6.900
|
1.39e-07
|
-1.260
|
| HMC_vs_Metro |
1
|
-8.774
|
1.18e-09
|
-1.602
|
| HMC_vs_Metro |
2
|
1.058
|
0.299
|
0.193
|
| HMC_vs_Metro |
3
|
4.238
|
0.000209
|
0.774
|
| HMC_vs_Metro |
4
|
2.237
|
0.0331
|
0.408
|
| HMC_vs_Metro |
5
|
-0.092
|
0.927
|
-0.017
|
| Metro_vs_DEMetro_Z |
0
|
5.964
|
1.76e-06
|
1.089
|
| Metro_vs_DEMetro_Z |
1
|
5.860
|
2.34e-06
|
1.070
|
| Metro_vs_DEMetro_Z |
2
|
1.312
|
0.2
|
0.240
|
| Metro_vs_DEMetro_Z |
3
|
-1.227
|
0.23
|
-0.224
|
| Metro_vs_DEMetro_Z |
4
|
-3.178
|
0.00351
|
-0.580
|
| Metro_vs_DEMetro_Z |
5
|
-0.458
|
0.65
|
-0.084
|
| HMC_vs_SMC |
0
|
3.521
|
0.00144
|
0.643
|
| HMC_vs_SMC |
1
|
5.166
|
1.6e-05
|
0.943
|
| HMC_vs_SMC |
2
|
5.663
|
4.03e-06
|
1.034
|
| HMC_vs_SMC |
3
|
7.206
|
6.21e-08
|
1.316
|
| HMC_vs_SMC |
4
|
5.930
|
1.93e-06
|
1.083
|
| HMC_vs_SMC |
5
|
5.224
|
1.36e-05
|
0.954
|
| Metro_vs_SMC |
0
|
8.045
|
7.15e-09
|
1.469
|
| Metro_vs_SMC |
1
|
10.607
|
1.71e-11
|
1.937
|
| Metro_vs_SMC |
2
|
8.162
|
5.33e-09
|
1.490
|
| Metro_vs_SMC |
3
|
8.759
|
1.22e-09
|
1.599
|
| Metro_vs_SMC |
4
|
12.202
|
6.04e-13
|
2.228
|
| Metro_vs_SMC |
5
|
9.579
|
1.74e-10
|
1.749
|
| HMC_vs_DEMetro_Z |
0
|
-2.363
|
0.0251
|
-0.431
|
| HMC_vs_DEMetro_Z |
1
|
-1.457
|
0.156
|
-0.266
|
| HMC_vs_DEMetro_Z |
2
|
2.020
|
0.0527
|
0.369
|
| HMC_vs_DEMetro_Z |
3
|
2.642
|
0.0132
|
0.482
|
| HMC_vs_DEMetro_Z |
4
|
0.188
|
0.852
|
0.034
|
| HMC_vs_DEMetro_Z |
5
|
-0.575
|
0.57
|
-0.105
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.022 |
0.016 |
0.008 |
0.677 |
| HMC |
4 |
0.024 |
0.014 |
0.005 |
1.853 |
| HMC |
6 |
0.053 |
0.014 |
0.005 |
8.687 |
| HMC |
8 |
0.150 |
0.014 |
0.006 |
23.751 |
| HMC |
10 |
0.154 |
0.013 |
0.006 |
21.933 |
| HMC |
12 |
0.152 |
0.014 |
0.006 |
23.065 |
| SMC |
0 |
0.014 |
0.016 |
0.008 |
-0.292 |
| SMC |
4 |
0.014 |
0.014 |
0.005 |
-0.114 |
| SMC |
6 |
0.017 |
0.014 |
0.005 |
0.681 |
| SMC |
8 |
0.013 |
0.014 |
0.006 |
-0.158 |
| SMC |
10 |
0.012 |
0.013 |
0.006 |
-0.054 |
| SMC |
12 |
0.012 |
0.014 |
0.006 |
-0.261 |
| Metro |
0 |
0.072 |
0.016 |
0.008 |
7.347 |
| Metro |
4 |
0.045 |
0.014 |
0.005 |
6.095 |
| Metro |
6 |
0.044 |
0.014 |
0.005 |
6.659 |
| Metro |
8 |
0.065 |
0.014 |
0.006 |
8.893 |
| Metro |
10 |
0.095 |
0.013 |
0.006 |
12.749 |
| Metro |
12 |
0.155 |
0.014 |
0.006 |
23.589 |
| DEMetro_Z |
0 |
0.028 |
0.016 |
0.008 |
1.579 |
| DEMetro_Z |
4 |
0.027 |
0.014 |
0.005 |
2.514 |
| DEMetro_Z |
6 |
0.039 |
0.014 |
0.005 |
5.440 |
| DEMetro_Z |
8 |
0.084 |
0.014 |
0.006 |
12.093 |
| DEMetro_Z |
10 |
0.149 |
0.013 |
0.006 |
21.070 |
| DEMetro_Z |
12 |
0.168 |
0.014 |
0.006 |
25.739 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
4.172 |
0.000116 |
1.340 |
| HMC |
4 |
2.535 |
0.0145 |
0.877 |
| HMC |
6 |
7.441 |
2.15e-08 |
7.195 |
| HMC |
8 |
9.013 |
6.2e-10 |
27.748 |
| HMC |
10 |
25.140 |
1.83e-21 |
51.048 |
| HMC |
12 |
140.313 |
3.49e-52 |
72.497 |
| SMC |
0 |
-1.147 |
0.256 |
-0.261 |
| SMC |
4 |
0.485 |
0.63 |
0.133 |
| SMC |
6 |
0.365 |
0.717 |
0.110 |
| SMC |
8 |
-0.546 |
0.588 |
-0.154 |
| SMC |
10 |
0.214 |
0.831 |
0.046 |
| SMC |
12 |
0.504 |
0.616 |
0.129 |
| Metro |
0 |
5.113 |
1.41e-05 |
4.122 |
| Metro |
4 |
5.297 |
7.82e-06 |
3.900 |
| Metro |
6 |
5.861 |
1.83e-06 |
5.874 |
| Metro |
8 |
6.304 |
5.45e-07 |
6.938 |
| Metro |
10 |
8.995 |
3.97e-10 |
9.396 |
| Metro |
12 |
8.637 |
1.55e-09 |
27.314 |
| DEMetro_Z |
0 |
1.233 |
0.223 |
0.429 |
| DEMetro_Z |
4 |
3.112 |
0.00342 |
1.404 |
| DEMetro_Z |
6 |
5.197 |
9.65e-06 |
3.401 |
| DEMetro_Z |
8 |
3.540 |
0.00136 |
8.732 |
| DEMetro_Z |
10 |
5.113 |
1.84e-05 |
22.534 |
| DEMetro_Z |
12 |
9.018 |
6.4e-10 |
51.072 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
2.249
|
0.0322
|
0.411
|
| HMC_vs_DEMetro_Z |
1
|
-0.955
|
0.348
|
-0.174
|
| HMC_vs_DEMetro_Z |
2
|
3.275
|
0.00274
|
0.598
|
| HMC_vs_DEMetro_Z |
3
|
4.939
|
3.01e-05
|
0.902
|
| HMC_vs_DEMetro_Z |
4
|
5.872
|
2.26e-06
|
1.072
|
| HMC_vs_DEMetro_Z |
5
|
3.678
|
0.000952
|
0.671
|
| Metro_vs_SMC |
0
|
5.645
|
4.24e-06
|
1.031
|
| Metro_vs_SMC |
1
|
4.947
|
2.94e-05
|
0.903
|
| Metro_vs_SMC |
2
|
5.615
|
4.6e-06
|
1.025
|
| Metro_vs_SMC |
3
|
6.241
|
8.25e-07
|
1.139
|
| Metro_vs_SMC |
4
|
8.935
|
7.96e-10
|
1.631
|
| Metro_vs_SMC |
5
|
8.662
|
1.54e-09
|
1.582
|
| Metro_vs_DEMetro_Z |
0
|
4.304
|
0.000174
|
0.786
|
| Metro_vs_DEMetro_Z |
1
|
3.006
|
0.00542
|
0.549
|
| Metro_vs_DEMetro_Z |
2
|
1.967
|
0.0589
|
0.359
|
| Metro_vs_DEMetro_Z |
3
|
-0.690
|
0.496
|
-0.126
|
| Metro_vs_DEMetro_Z |
4
|
-2.752
|
0.0101
|
-0.503
|
| Metro_vs_DEMetro_Z |
5
|
-4.293
|
0.00018
|
-0.784
|
| HMC_vs_Metro |
0
|
-3.470
|
0.00165
|
-0.634
|
| HMC_vs_Metro |
1
|
-4.218
|
0.00022
|
-0.770
|
| HMC_vs_Metro |
2
|
0.917
|
0.367
|
0.167
|
| HMC_vs_Metro |
3
|
6.689
|
2.45e-07
|
1.221
|
| HMC_vs_Metro |
4
|
20.033
|
1.57e-18
|
3.657
|
| HMC_vs_Metro |
5
|
13.931
|
2.22e-14
|
2.543
|
| HMC_vs_SMC |
0
|
5.682
|
3.82e-06
|
1.037
|
| HMC_vs_SMC |
1
|
1.781
|
0.0854
|
0.325
|
| HMC_vs_SMC |
2
|
7.355
|
4.21e-08
|
1.343
|
| HMC_vs_SMC |
3
|
9.081
|
5.62e-10
|
1.658
|
| HMC_vs_SMC |
4
|
24.998
|
3.6e-21
|
4.564
|
| HMC_vs_SMC |
5
|
142.504
|
7.98e-43
|
26.017
|
| DEMetro_Z_vs_SMC |
0
|
2.103
|
0.0443
|
0.384
|
| DEMetro_Z_vs_SMC |
1
|
2.877
|
0.00746
|
0.525
|
| DEMetro_Z_vs_SMC |
2
|
5.676
|
3.89e-06
|
1.036
|
| DEMetro_Z_vs_SMC |
3
|
3.706
|
0.000884
|
0.677
|
| DEMetro_Z_vs_SMC |
4
|
5.084
|
2.01e-05
|
0.928
|
| DEMetro_Z_vs_SMC |
5
|
8.981
|
7.12e-10
|
1.640
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.044 |
0.023 |
0.016 |
1.340 |
| HMC |
4 |
0.033 |
0.022 |
0.013 |
0.877 |
| HMC |
6 |
0.100 |
0.020 |
0.011 |
7.195 |
| HMC |
8 |
0.457 |
0.026 |
0.016 |
27.748 |
| HMC |
10 |
1.040 |
0.026 |
0.020 |
51.048 |
| HMC |
12 |
1.328 |
0.030 |
0.018 |
72.497 |
| SMC |
0 |
0.019 |
0.023 |
0.016 |
-0.261 |
| SMC |
4 |
0.023 |
0.022 |
0.013 |
0.133 |
| SMC |
6 |
0.021 |
0.020 |
0.011 |
0.110 |
| SMC |
8 |
0.024 |
0.026 |
0.016 |
-0.154 |
| SMC |
10 |
0.027 |
0.026 |
0.020 |
0.046 |
| SMC |
12 |
0.032 |
0.030 |
0.018 |
0.129 |
| Metro |
0 |
0.088 |
0.023 |
0.016 |
4.122 |
| Metro |
4 |
0.072 |
0.022 |
0.013 |
3.900 |
| Metro |
6 |
0.085 |
0.020 |
0.011 |
5.874 |
| Metro |
8 |
0.134 |
0.026 |
0.016 |
6.938 |
| Metro |
10 |
0.213 |
0.026 |
0.020 |
9.396 |
| Metro |
12 |
0.519 |
0.030 |
0.018 |
27.314 |
| DEMetro_Z |
0 |
0.030 |
0.023 |
0.016 |
0.429 |
| DEMetro_Z |
4 |
0.040 |
0.022 |
0.013 |
1.404 |
| DEMetro_Z |
6 |
0.057 |
0.020 |
0.011 |
3.401 |
| DEMetro_Z |
8 |
0.162 |
0.026 |
0.016 |
8.732 |
| DEMetro_Z |
10 |
0.474 |
0.026 |
0.020 |
22.534 |
| DEMetro_Z |
12 |
0.944 |
0.030 |
0.018 |
51.072 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
2.148 |
0.038 |
1.002 |
| HMC |
4 |
4.729 |
2.82e-05 |
2.141 |
| HMC |
6 |
3.881 |
0.000366 |
1.654 |
| HMC |
8 |
5.894 |
2.01e-06 |
12.406 |
| HMC |
10 |
21.423 |
1.61e-19 |
43.355 |
| HMC |
12 |
202.607 |
2.3e-82 |
57.462 |
| SMC |
0 |
-0.718 |
0.476 |
-0.179 |
| SMC |
4 |
1.164 |
0.25 |
0.377 |
| SMC |
6 |
-0.902 |
0.371 |
-0.251 |
| SMC |
8 |
0.803 |
0.425 |
0.225 |
| SMC |
10 |
-0.380 |
0.706 |
-0.097 |
| SMC |
12 |
-0.311 |
0.757 |
-0.071 |
| Metro |
0 |
4.993 |
2.14e-05 |
4.696 |
| Metro |
4 |
5.051 |
1.34e-05 |
2.927 |
| Metro |
6 |
4.158 |
0.000214 |
2.961 |
| Metro |
8 |
5.975 |
1.14e-06 |
4.764 |
| Metro |
10 |
7.451 |
1.68e-08 |
5.882 |
| Metro |
12 |
6.247 |
7.58e-07 |
12.927 |
| DEMetro_Z |
0 |
3.131 |
0.00334 |
1.541 |
| DEMetro_Z |
4 |
4.840 |
2.19e-05 |
2.394 |
| DEMetro_Z |
6 |
4.600 |
4.26e-05 |
2.101 |
| DEMetro_Z |
8 |
2.722 |
0.0107 |
3.670 |
| DEMetro_Z |
10 |
4.626 |
7.1e-05 |
17.411 |
| DEMetro_Z |
12 |
8.129 |
5.66e-09 |
39.436 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.658
|
0.0126
|
0.485
|
| HMC_vs_SMC |
1
|
5.065
|
2.12e-05
|
0.925
|
| HMC_vs_SMC |
2
|
4.943
|
2.97e-05
|
0.902
|
| HMC_vs_SMC |
3
|
5.891
|
2.15e-06
|
1.076
|
| HMC_vs_SMC |
4
|
21.820
|
1.53e-19
|
3.984
|
| HMC_vs_SMC |
5
|
196.745
|
6.98e-47
|
35.921
|
| Metro_vs_DEMetro_Z |
0
|
3.015
|
0.0053
|
0.550
|
| Metro_vs_DEMetro_Z |
1
|
0.757
|
0.455
|
0.138
|
| Metro_vs_DEMetro_Z |
2
|
1.072
|
0.292
|
0.196
|
| Metro_vs_DEMetro_Z |
3
|
0.725
|
0.474
|
0.132
|
| Metro_vs_DEMetro_Z |
4
|
-2.891
|
0.00721
|
-0.528
|
| Metro_vs_DEMetro_Z |
5
|
-5.784
|
2.89e-06
|
-1.056
|
| HMC_vs_Metro |
0
|
-3.342
|
0.0023
|
-0.610
|
| HMC_vs_Metro |
1
|
-1.179
|
0.248
|
-0.215
|
| HMC_vs_Metro |
2
|
-1.715
|
0.097
|
-0.313
|
| HMC_vs_Metro |
3
|
3.552
|
0.00133
|
0.649
|
| HMC_vs_Metro |
4
|
19.677
|
2.55e-18
|
3.592
|
| HMC_vs_Metro |
5
|
21.952
|
1.3e-19
|
4.008
|
| HMC_vs_DEMetro_Z |
0
|
-0.804
|
0.428
|
-0.147
|
| HMC_vs_DEMetro_Z |
1
|
-0.367
|
0.716
|
-0.067
|
| HMC_vs_DEMetro_Z |
2
|
-0.748
|
0.46
|
-0.137
|
| HMC_vs_DEMetro_Z |
3
|
3.432
|
0.00182
|
0.627
|
| HMC_vs_DEMetro_Z |
4
|
5.797
|
2.78e-06
|
1.058
|
| HMC_vs_DEMetro_Z |
5
|
3.804
|
0.00068
|
0.694
|
| Metro_vs_SMC |
0
|
4.970
|
2.76e-05
|
0.907
|
| Metro_vs_SMC |
1
|
4.686
|
6.07e-05
|
0.856
|
| Metro_vs_SMC |
2
|
4.318
|
0.000168
|
0.788
|
| Metro_vs_SMC |
3
|
5.876
|
2.24e-06
|
1.073
|
| Metro_vs_SMC |
4
|
7.260
|
5.39e-08
|
1.326
|
| Metro_vs_SMC |
5
|
6.386
|
5.55e-07
|
1.166
|
| DEMetro_Z_vs_SMC |
0
|
3.287
|
0.00265
|
0.600
|
| DEMetro_Z_vs_SMC |
1
|
3.614
|
0.00113
|
0.660
|
| DEMetro_Z_vs_SMC |
2
|
5.124
|
1.8e-05
|
0.936
|
| DEMetro_Z_vs_SMC |
3
|
2.522
|
0.0174
|
0.461
|
| DEMetro_Z_vs_SMC |
4
|
4.634
|
7.01e-05
|
0.846
|
| DEMetro_Z_vs_SMC |
5
|
8.174
|
5.17e-09
|
1.492
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.044 |
0.028 |
0.016 |
1.002 |
| HMC |
4 |
0.067 |
0.029 |
0.017 |
2.141 |
| HMC |
6 |
0.081 |
0.044 |
0.022 |
1.654 |
| HMC |
8 |
0.406 |
0.047 |
0.029 |
12.406 |
| HMC |
10 |
1.618 |
0.054 |
0.036 |
43.355 |
| HMC |
12 |
2.476 |
0.065 |
0.042 |
57.462 |
| SMC |
0 |
0.025 |
0.028 |
0.016 |
-0.179 |
| SMC |
4 |
0.036 |
0.029 |
0.017 |
0.377 |
| SMC |
6 |
0.038 |
0.044 |
0.022 |
-0.251 |
| SMC |
8 |
0.054 |
0.047 |
0.029 |
0.225 |
| SMC |
10 |
0.050 |
0.054 |
0.036 |
-0.097 |
| SMC |
12 |
0.062 |
0.065 |
0.042 |
-0.071 |
| Metro |
0 |
0.102 |
0.028 |
0.016 |
4.696 |
| Metro |
4 |
0.080 |
0.029 |
0.017 |
2.927 |
| Metro |
6 |
0.110 |
0.044 |
0.022 |
2.961 |
| Metro |
8 |
0.185 |
0.047 |
0.029 |
4.764 |
| Metro |
10 |
0.266 |
0.054 |
0.036 |
5.882 |
| Metro |
12 |
0.607 |
0.065 |
0.042 |
12.927 |
| DEMetro_Z |
0 |
0.052 |
0.028 |
0.016 |
1.541 |
| DEMetro_Z |
4 |
0.071 |
0.029 |
0.017 |
2.394 |
| DEMetro_Z |
6 |
0.091 |
0.044 |
0.022 |
2.101 |
| DEMetro_Z |
8 |
0.153 |
0.047 |
0.029 |
3.670 |
| DEMetro_Z |
10 |
0.682 |
0.054 |
0.036 |
17.411 |
| DEMetro_Z |
12 |
1.720 |
0.065 |
0.042 |
39.436 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
4.485 |
4.4e-05 |
1.529 |
| HMC |
4 |
4.543 |
4.34e-05 |
1.793 |
| HMC |
6 |
7.683 |
1.39e-08 |
10.119 |
| HMC |
8 |
8.845 |
9.51e-10 |
34.358 |
| HMC |
10 |
24.013 |
8.67e-21 |
71.103 |
| HMC |
12 |
64.023 |
1.1e-33 |
87.862 |
| SMC |
0 |
-1.485 |
0.144 |
-0.327 |
| SMC |
4 |
0.619 |
0.539 |
0.181 |
| SMC |
6 |
0.409 |
0.685 |
0.136 |
| SMC |
8 |
-0.489 |
0.626 |
-0.131 |
| SMC |
10 |
0.443 |
0.659 |
0.103 |
| SMC |
12 |
-0.422 |
0.674 |
-0.105 |
| Metro |
0 |
7.338 |
2.5e-08 |
6.227 |
| Metro |
4 |
6.817 |
1.21e-07 |
6.670 |
| Metro |
6 |
8.418 |
1.91e-09 |
9.865 |
| Metro |
8 |
8.810 |
7.19e-10 |
10.529 |
| Metro |
10 |
10.388 |
1.81e-11 |
14.012 |
| Metro |
12 |
9.092 |
5.22e-10 |
33.475 |
| DEMetro_Z |
0 |
4.129 |
0.000146 |
1.456 |
| DEMetro_Z |
4 |
7.771 |
1.41e-09 |
3.385 |
| DEMetro_Z |
6 |
7.699 |
8.52e-09 |
6.129 |
| DEMetro_Z |
8 |
3.702 |
0.000887 |
12.405 |
| DEMetro_Z |
10 |
5.266 |
1.2e-05 |
32.599 |
| DEMetro_Z |
12 |
8.945 |
7.69e-10 |
63.349 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
5.519
|
6e-06
|
1.008
|
| Metro_vs_DEMetro_Z |
1
|
3.081
|
0.00448
|
0.563
|
| Metro_vs_DEMetro_Z |
2
|
2.567
|
0.0157
|
0.469
|
| Metro_vs_DEMetro_Z |
3
|
-0.542
|
0.592
|
-0.099
|
| Metro_vs_DEMetro_Z |
4
|
-2.780
|
0.00945
|
-0.508
|
| Metro_vs_DEMetro_Z |
5
|
-4.291
|
0.000181
|
-0.783
|
| DEMetro_Z_vs_SMC |
0
|
5.323
|
1.03e-05
|
0.972
|
| DEMetro_Z_vs_SMC |
1
|
6.962
|
1.18e-07
|
1.271
|
| DEMetro_Z_vs_SMC |
2
|
7.981
|
8.42e-09
|
1.457
|
| DEMetro_Z_vs_SMC |
3
|
3.807
|
0.000674
|
0.695
|
| DEMetro_Z_vs_SMC |
4
|
5.215
|
1.39e-05
|
0.952
|
| DEMetro_Z_vs_SMC |
5
|
8.949
|
7.69e-10
|
1.634
|
| HMC_vs_DEMetro_Z |
0
|
0.174
|
0.863
|
0.032
|
| HMC_vs_DEMetro_Z |
1
|
-2.665
|
0.0125
|
-0.487
|
| HMC_vs_DEMetro_Z |
2
|
2.546
|
0.0165
|
0.465
|
| HMC_vs_DEMetro_Z |
3
|
4.375
|
0.000143
|
0.799
|
| HMC_vs_DEMetro_Z |
4
|
5.409
|
8.15e-06
|
0.987
|
| HMC_vs_DEMetro_Z |
5
|
3.342
|
0.0023
|
0.610
|
| HMC_vs_Metro |
0
|
-5.569
|
5.23e-06
|
-1.017
|
| HMC_vs_Metro |
1
|
-5.222
|
1.37e-05
|
-0.953
|
| HMC_vs_Metro |
2
|
0.134
|
0.895
|
0.024
|
| HMC_vs_Metro |
3
|
6.158
|
1.03e-06
|
1.124
|
| HMC_vs_Metro |
4
|
19.587
|
2.89e-18
|
3.576
|
| HMC_vs_Metro |
5
|
15.547
|
1.33e-15
|
2.838
|
| HMC_vs_SMC |
0
|
6.569
|
3.39e-07
|
1.199
|
| HMC_vs_SMC |
1
|
3.416
|
0.0019
|
0.624
|
| HMC_vs_SMC |
2
|
7.727
|
1.61e-08
|
1.411
|
| HMC_vs_SMC |
3
|
8.908
|
8.49e-10
|
1.626
|
| HMC_vs_SMC |
4
|
24.115
|
9.74e-21
|
4.403
|
| HMC_vs_SMC |
5
|
66.007
|
3.66e-33
|
12.051
|
| Metro_vs_SMC |
0
|
7.829
|
1.24e-08
|
1.429
|
| Metro_vs_SMC |
1
|
6.282
|
7.37e-07
|
1.147
|
| Metro_vs_SMC |
2
|
8.025
|
7.52e-09
|
1.465
|
| Metro_vs_SMC |
3
|
8.673
|
1.5e-09
|
1.583
|
| Metro_vs_SMC |
4
|
10.336
|
3.1e-11
|
1.887
|
| Metro_vs_SMC |
5
|
9.118
|
5.14e-10
|
1.665
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.047 |
0.030 |
0.011 |
1.529 |
| HMC |
4 |
0.044 |
0.030 |
0.008 |
1.793 |
| HMC |
6 |
0.100 |
0.031 |
0.007 |
10.119 |
| HMC |
8 |
0.409 |
0.036 |
0.011 |
34.358 |
| HMC |
10 |
0.945 |
0.036 |
0.013 |
71.103 |
| HMC |
12 |
1.195 |
0.043 |
0.013 |
87.862 |
| SMC |
0 |
0.026 |
0.030 |
0.011 |
-0.327 |
| SMC |
4 |
0.031 |
0.030 |
0.008 |
0.181 |
| SMC |
6 |
0.032 |
0.031 |
0.007 |
0.136 |
| SMC |
8 |
0.035 |
0.036 |
0.011 |
-0.131 |
| SMC |
10 |
0.038 |
0.036 |
0.013 |
0.103 |
| SMC |
12 |
0.041 |
0.043 |
0.013 |
-0.105 |
| Metro |
0 |
0.099 |
0.030 |
0.011 |
6.227 |
| Metro |
4 |
0.080 |
0.030 |
0.008 |
6.670 |
| Metro |
6 |
0.098 |
0.031 |
0.007 |
9.865 |
| Metro |
8 |
0.151 |
0.036 |
0.011 |
10.529 |
| Metro |
10 |
0.216 |
0.036 |
0.013 |
14.012 |
| Metro |
12 |
0.482 |
0.043 |
0.013 |
33.475 |
| DEMetro_Z |
0 |
0.046 |
0.030 |
0.011 |
1.456 |
| DEMetro_Z |
4 |
0.056 |
0.030 |
0.008 |
3.385 |
| DEMetro_Z |
6 |
0.073 |
0.031 |
0.007 |
6.129 |
| DEMetro_Z |
8 |
0.171 |
0.036 |
0.011 |
12.405 |
| DEMetro_Z |
10 |
0.453 |
0.036 |
0.013 |
32.599 |
| DEMetro_Z |
12 |
0.873 |
0.043 |
0.013 |
63.349 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
3.087 |
0.00325 |
0.993 |
| HMC |
4 |
4.341 |
7.63e-05 |
1.587 |
| HMC |
6 |
7.146 |
5.15e-08 |
7.533 |
| HMC |
8 |
8.757 |
1.18e-09 |
33.214 |
| HMC |
10 |
24.583 |
4.15e-21 |
62.753 |
| HMC |
12 |
160.963 |
2.48e-55 |
79.780 |
| SMC |
0 |
-1.319 |
0.193 |
-0.299 |
| SMC |
4 |
0.303 |
0.763 |
0.084 |
| SMC |
6 |
-0.310 |
0.758 |
-0.088 |
| SMC |
8 |
-0.572 |
0.57 |
-0.142 |
| SMC |
10 |
0.550 |
0.584 |
0.127 |
| SMC |
12 |
-0.756 |
0.453 |
-0.175 |
| Metro |
0 |
7.359 |
1.83e-08 |
5.181 |
| Metro |
4 |
6.496 |
2.11e-07 |
4.412 |
| Metro |
6 |
7.781 |
7.76e-09 |
6.858 |
| Metro |
8 |
9.545 |
7.71e-11 |
8.260 |
| Metro |
10 |
10.428 |
1.38e-11 |
11.792 |
| Metro |
12 |
9.144 |
4.51e-10 |
27.909 |
| DEMetro_Z |
0 |
3.342 |
0.00161 |
1.164 |
| DEMetro_Z |
4 |
7.360 |
1.9e-09 |
2.530 |
| DEMetro_Z |
6 |
6.842 |
6.44e-08 |
4.177 |
| DEMetro_Z |
8 |
3.700 |
0.000889 |
10.623 |
| DEMetro_Z |
10 |
5.200 |
1.45e-05 |
27.998 |
| DEMetro_Z |
12 |
8.960 |
7.38e-10 |
55.514 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.620
|
7.29e-05
|
0.843
|
| DEMetro_Z_vs_SMC |
1
|
6.775
|
1.95e-07
|
1.237
|
| DEMetro_Z_vs_SMC |
2
|
7.229
|
5.85e-08
|
1.320
|
| DEMetro_Z_vs_SMC |
3
|
3.791
|
0.000703
|
0.692
|
| DEMetro_Z_vs_SMC |
4
|
5.152
|
1.66e-05
|
0.941
|
| DEMetro_Z_vs_SMC |
5
|
9.002
|
6.77e-10
|
1.644
|
| HMC_vs_Metro |
0
|
-5.934
|
1.91e-06
|
-1.083
|
| HMC_vs_Metro |
1
|
-4.123
|
0.000286
|
-0.753
|
| HMC_vs_Metro |
2
|
0.453
|
0.654
|
0.083
|
| HMC_vs_Metro |
3
|
6.730
|
2.2e-07
|
1.229
|
| HMC_vs_Metro |
4
|
20.699
|
6.46e-19
|
3.779
|
| HMC_vs_Metro |
5
|
16.956
|
1.37e-16
|
3.096
|
| Metro_vs_DEMetro_Z |
0
|
5.302
|
1.1e-05
|
0.968
|
| Metro_vs_DEMetro_Z |
1
|
2.648
|
0.013
|
0.483
|
| Metro_vs_DEMetro_Z |
2
|
2.498
|
0.0184
|
0.456
|
| Metro_vs_DEMetro_Z |
3
|
-0.795
|
0.433
|
-0.145
|
| Metro_vs_DEMetro_Z |
4
|
-2.802
|
0.00894
|
-0.512
|
| Metro_vs_DEMetro_Z |
5
|
-4.625
|
7.19e-05
|
-0.844
|
| HMC_vs_SMC |
0
|
5.022
|
2.38e-05
|
0.917
|
| HMC_vs_SMC |
1
|
3.836
|
0.000624
|
0.700
|
| HMC_vs_SMC |
2
|
7.452
|
3.27e-08
|
1.360
|
| HMC_vs_SMC |
3
|
8.839
|
1e-09
|
1.614
|
| HMC_vs_SMC |
4
|
24.600
|
5.61e-21
|
4.491
|
| HMC_vs_SMC |
5
|
175.861
|
1.8e-45
|
32.108
|
| Metro_vs_SMC |
0
|
7.942
|
9.28e-09
|
1.450
|
| Metro_vs_SMC |
1
|
5.998
|
1.6e-06
|
1.095
|
| Metro_vs_SMC |
2
|
8.109
|
6.08e-09
|
1.481
|
| Metro_vs_SMC |
3
|
9.544
|
1.88e-10
|
1.742
|
| Metro_vs_SMC |
4
|
10.436
|
2.48e-11
|
1.905
|
| Metro_vs_SMC |
5
|
9.274
|
3.54e-10
|
1.693
|
| HMC_vs_DEMetro_Z |
0
|
-0.425
|
0.674
|
-0.078
|
| HMC_vs_DEMetro_Z |
1
|
-2.062
|
0.0483
|
-0.376
|
| HMC_vs_DEMetro_Z |
2
|
2.680
|
0.012
|
0.489
|
| HMC_vs_DEMetro_Z |
3
|
4.685
|
6.09e-05
|
0.855
|
| HMC_vs_DEMetro_Z |
4
|
5.695
|
3.68e-06
|
1.040
|
| HMC_vs_DEMetro_Z |
5
|
3.901
|
0.000523
|
0.712
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.024 |
0.016 |
0.008 |
0.993 |
| HMC |
4 |
0.022 |
0.014 |
0.005 |
1.587 |
| HMC |
6 |
0.048 |
0.014 |
0.005 |
7.533 |
| HMC |
8 |
0.205 |
0.014 |
0.006 |
33.214 |
| HMC |
10 |
0.418 |
0.013 |
0.006 |
62.753 |
| HMC |
12 |
0.491 |
0.014 |
0.006 |
79.780 |
| SMC |
0 |
0.014 |
0.016 |
0.008 |
-0.299 |
| SMC |
4 |
0.015 |
0.014 |
0.005 |
0.084 |
| SMC |
6 |
0.013 |
0.014 |
0.005 |
-0.088 |
| SMC |
8 |
0.013 |
0.014 |
0.006 |
-0.142 |
| SMC |
10 |
0.013 |
0.013 |
0.006 |
0.127 |
| SMC |
12 |
0.013 |
0.014 |
0.006 |
-0.175 |
| Metro |
0 |
0.055 |
0.016 |
0.008 |
5.181 |
| Metro |
4 |
0.036 |
0.014 |
0.005 |
4.412 |
| Metro |
6 |
0.045 |
0.014 |
0.005 |
6.858 |
| Metro |
8 |
0.062 |
0.014 |
0.006 |
8.260 |
| Metro |
10 |
0.089 |
0.013 |
0.006 |
11.792 |
| Metro |
12 |
0.181 |
0.014 |
0.006 |
27.909 |
| DEMetro_Z |
0 |
0.025 |
0.016 |
0.008 |
1.164 |
| DEMetro_Z |
4 |
0.027 |
0.014 |
0.005 |
2.530 |
| DEMetro_Z |
6 |
0.033 |
0.014 |
0.005 |
4.177 |
| DEMetro_Z |
8 |
0.075 |
0.014 |
0.006 |
10.623 |
| DEMetro_Z |
10 |
0.193 |
0.013 |
0.006 |
27.998 |
| DEMetro_Z |
12 |
0.346 |
0.014 |
0.006 |
55.514 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_heavy_Tails
(Mixture,
mm,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
1.309 |
0.196 |
0.369 |
| HMC |
4 |
2.758 |
0.00818 |
0.952 |
| HMC |
6 |
2.352 |
0.0233 |
0.950 |
| HMC |
8 |
5.365 |
4.25e-06 |
2.652 |
| HMC |
10 |
5.048 |
1.75e-05 |
4.257 |
| HMC |
12 |
6.347 |
3.09e-07 |
4.130 |
| SMC |
0 |
3.351 |
0.00149 |
1.044 |
| SMC |
4 |
3.398 |
0.00165 |
1.798 |
| SMC |
6 |
3.536 |
0.00113 |
1.910 |
| SMC |
8 |
3.976 |
0.000302 |
1.952 |
| SMC |
10 |
3.772 |
0.000643 |
2.762 |
| SMC |
12 |
3.930 |
0.000355 |
2.017 |
| Metro |
0 |
2.556 |
0.0147 |
1.241 |
| Metro |
4 |
2.730 |
0.0102 |
2.131 |
| Metro |
6 |
2.695 |
0.0104 |
1.294 |
| Metro |
8 |
3.196 |
0.00253 |
1.189 |
| Metro |
10 |
4.326 |
0.000104 |
2.070 |
| Metro |
12 |
4.938 |
8.59e-06 |
1.572 |
| DEMetro_Z |
0 |
5.316 |
5.84e-06 |
3.000 |
| DEMetro_Z |
4 |
5.470 |
4.05e-06 |
3.395 |
| DEMetro_Z |
6 |
4.180 |
0.000137 |
1.641 |
| DEMetro_Z |
8 |
4.581 |
6.79e-05 |
3.928 |
| DEMetro_Z |
10 |
5.740 |
2.67e-06 |
6.201 |
| DEMetro_Z |
12 |
7.000 |
4.97e-08 |
4.835 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-4.396
|
0.000135
|
-0.803
|
| HMC_vs_DEMetro_Z |
1
|
-3.834
|
0.000627
|
-0.700
|
| HMC_vs_DEMetro_Z |
2
|
-1.337
|
0.191
|
-0.244
|
| HMC_vs_DEMetro_Z |
3
|
-1.384
|
0.177
|
-0.253
|
| HMC_vs_DEMetro_Z |
4
|
-1.571
|
0.127
|
-0.287
|
| HMC_vs_DEMetro_Z |
5
|
-0.831
|
0.413
|
-0.152
|
| Metro_vs_SMC |
0
|
0.395
|
0.696
|
0.072
|
| Metro_vs_SMC |
1
|
0.387
|
0.702
|
0.071
|
| Metro_vs_SMC |
2
|
-0.891
|
0.38
|
-0.163
|
| Metro_vs_SMC |
3
|
-1.360
|
0.184
|
-0.248
|
| Metro_vs_SMC |
4
|
-0.745
|
0.462
|
-0.136
|
| Metro_vs_SMC |
5
|
-0.802
|
0.429
|
-0.147
|
| Metro_vs_DEMetro_Z |
0
|
-2.558
|
0.016
|
-0.467
|
| Metro_vs_DEMetro_Z |
1
|
-1.491
|
0.147
|
-0.272
|
| Metro_vs_DEMetro_Z |
2
|
-0.644
|
0.524
|
-0.118
|
| Metro_vs_DEMetro_Z |
3
|
-2.810
|
0.00878
|
-0.513
|
| Metro_vs_DEMetro_Z |
4
|
-3.709
|
0.000876
|
-0.677
|
| Metro_vs_DEMetro_Z |
5
|
-4.432
|
0.000122
|
-0.809
|
| HMC_vs_Metro |
0
|
-1.604
|
0.12
|
-0.293
|
| HMC_vs_Metro |
1
|
-1.678
|
0.104
|
-0.306
|
| HMC_vs_Metro |
2
|
-0.704
|
0.487
|
-0.129
|
| HMC_vs_Metro |
3
|
2.134
|
0.0415
|
0.390
|
| HMC_vs_Metro |
4
|
2.301
|
0.0287
|
0.420
|
| HMC_vs_Metro |
5
|
3.637
|
0.00106
|
0.664
|
| HMC_vs_SMC |
0
|
-2.082
|
0.0463
|
-0.380
|
| HMC_vs_SMC |
1
|
-1.476
|
0.151
|
-0.269
|
| HMC_vs_SMC |
2
|
-1.664
|
0.107
|
-0.304
|
| HMC_vs_SMC |
3
|
0.960
|
0.345
|
0.175
|
| HMC_vs_SMC |
4
|
1.477
|
0.151
|
0.270
|
| HMC_vs_SMC |
5
|
2.654
|
0.0128
|
0.484
|
| DEMetro_Z_vs_SMC |
0
|
3.485
|
0.00159
|
0.636
|
| DEMetro_Z_vs_SMC |
1
|
2.194
|
0.0364
|
0.401
|
| DEMetro_Z_vs_SMC |
2
|
-0.419
|
0.678
|
-0.077
|
| DEMetro_Z_vs_SMC |
3
|
1.983
|
0.0569
|
0.362
|
| DEMetro_Z_vs_SMC |
4
|
2.237
|
0.0332
|
0.408
|
| DEMetro_Z_vs_SMC |
5
|
3.596
|
0.00118
|
0.657
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.067 |
0.056 |
0.031 |
0.369 |
| HMC |
4 |
0.081 |
0.056 |
0.026 |
0.952 |
| HMC |
6 |
0.133 |
0.084 |
0.051 |
0.950 |
| HMC |
8 |
0.234 |
0.080 |
0.058 |
2.652 |
| HMC |
10 |
0.329 |
0.096 |
0.055 |
4.257 |
| HMC |
12 |
0.535 |
0.091 |
0.108 |
4.130 |
| SMC |
0 |
0.088 |
0.056 |
0.031 |
1.044 |
| SMC |
4 |
0.103 |
0.056 |
0.026 |
1.798 |
| SMC |
6 |
0.182 |
0.084 |
0.051 |
1.910 |
| SMC |
8 |
0.193 |
0.080 |
0.058 |
1.952 |
| SMC |
10 |
0.247 |
0.096 |
0.055 |
2.762 |
| SMC |
12 |
0.308 |
0.091 |
0.108 |
2.017 |
| Metro |
0 |
0.094 |
0.056 |
0.031 |
1.241 |
| Metro |
4 |
0.111 |
0.056 |
0.026 |
2.131 |
| Metro |
6 |
0.150 |
0.084 |
0.051 |
1.294 |
| Metro |
8 |
0.149 |
0.080 |
0.058 |
1.189 |
| Metro |
10 |
0.210 |
0.096 |
0.055 |
2.070 |
| Metro |
12 |
0.260 |
0.091 |
0.108 |
1.572 |
| DEMetro_Z |
0 |
0.149 |
0.056 |
0.031 |
3.000 |
| DEMetro_Z |
4 |
0.144 |
0.056 |
0.026 |
3.395 |
| DEMetro_Z |
6 |
0.168 |
0.084 |
0.051 |
1.641 |
| DEMetro_Z |
8 |
0.308 |
0.080 |
0.058 |
3.928 |
| DEMetro_Z |
10 |
0.435 |
0.096 |
0.055 |
6.201 |
| DEMetro_Z |
12 |
0.611 |
0.091 |
0.108 |
4.835 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
-1.293 |
0.206 |
-0.239 |
| HMC |
4 |
-1.207 |
0.236 |
-0.229 |
| HMC |
6 |
-1.460 |
0.154 |
-0.272 |
| HMC |
8 |
-0.548 |
0.586 |
-0.123 |
| HMC |
10 |
-0.913 |
0.365 |
-0.214 |
| HMC |
12 |
-0.981 |
0.335 |
-0.179 |
| SMC |
0 |
-0.898 |
0.376 |
-0.165 |
| SMC |
4 |
-0.267 |
0.791 |
-0.050 |
| SMC |
6 |
-1.631 |
0.114 |
-0.299 |
| SMC |
8 |
-0.813 |
0.421 |
-0.159 |
| SMC |
10 |
-1.725 |
0.0939 |
-0.325 |
| SMC |
12 |
-0.984 |
0.333 |
-0.180 |
| Metro |
0 |
-1.449 |
0.158 |
-0.265 |
| Metro |
4 |
-1.421 |
0.165 |
-0.264 |
| Metro |
6 |
-1.373 |
0.18 |
-0.254 |
| Metro |
8 |
-0.715 |
0.479 |
-0.141 |
| Metro |
10 |
-1.676 |
0.103 |
-0.316 |
| Metro |
12 |
-0.968 |
0.341 |
-0.177 |
| DEMetro_Z |
0 |
-1.155 |
0.257 |
-0.214 |
| DEMetro_Z |
4 |
-1.266 |
0.215 |
-0.235 |
| DEMetro_Z |
6 |
-1.483 |
0.149 |
-0.273 |
| DEMetro_Z |
8 |
-0.607 |
0.547 |
-0.122 |
| DEMetro_Z |
10 |
-1.390 |
0.174 |
-0.259 |
| DEMetro_Z |
12 |
-0.961 |
0.345 |
-0.175 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-1.959
|
0.0598
|
-0.358
|
| HMC_vs_SMC |
1
|
-2.939
|
0.00641
|
-0.537
|
| HMC_vs_SMC |
2
|
0.783
|
0.44
|
0.143
|
| HMC_vs_SMC |
3
|
0.348
|
0.73
|
0.064
|
| HMC_vs_SMC |
4
|
0.790
|
0.436
|
0.144
|
| HMC_vs_SMC |
5
|
0.186
|
0.854
|
0.034
|
| Metro_vs_DEMetro_Z |
0
|
-1.860
|
0.0731
|
-0.340
|
| Metro_vs_DEMetro_Z |
1
|
-1.576
|
0.126
|
-0.288
|
| Metro_vs_DEMetro_Z |
2
|
0.762
|
0.452
|
0.139
|
| Metro_vs_DEMetro_Z |
3
|
-0.466
|
0.645
|
-0.085
|
| Metro_vs_DEMetro_Z |
4
|
-1.510
|
0.142
|
-0.276
|
| Metro_vs_DEMetro_Z |
5
|
-0.791
|
0.435
|
-0.144
|
| HMC_vs_Metro |
0
|
0.925
|
0.363
|
0.169
|
| HMC_vs_Metro |
1
|
0.711
|
0.483
|
0.130
|
| HMC_vs_Metro |
2
|
-0.442
|
0.662
|
-0.081
|
| HMC_vs_Metro |
3
|
0.155
|
0.878
|
0.028
|
| HMC_vs_Metro |
4
|
0.820
|
0.419
|
0.150
|
| HMC_vs_Metro |
5
|
-1.329
|
0.194
|
-0.243
|
| HMC_vs_DEMetro_Z |
0
|
-0.631
|
0.533
|
-0.115
|
| HMC_vs_DEMetro_Z |
1
|
0.131
|
0.896
|
0.024
|
| HMC_vs_DEMetro_Z |
2
|
0.008
|
0.994
|
0.001
|
| HMC_vs_DEMetro_Z |
3
|
-0.006
|
0.995
|
-0.001
|
| HMC_vs_DEMetro_Z |
4
|
0.366
|
0.717
|
0.067
|
| HMC_vs_DEMetro_Z |
5
|
-2.908
|
0.00692
|
-0.531
|
| Metro_vs_SMC |
0
|
-4.134
|
0.000278
|
-0.755
|
| Metro_vs_SMC |
1
|
-3.909
|
0.000512
|
-0.714
|
| Metro_vs_SMC |
2
|
1.812
|
0.0804
|
0.331
|
| Metro_vs_SMC |
3
|
0.255
|
0.801
|
0.046
|
| Metro_vs_SMC |
4
|
0.161
|
0.874
|
0.029
|
| Metro_vs_SMC |
5
|
1.082
|
0.288
|
0.197
|
| DEMetro_Z_vs_SMC |
0
|
-1.754
|
0.09
|
-0.320
|
| DEMetro_Z_vs_SMC |
1
|
-3.258
|
0.00286
|
-0.595
|
| DEMetro_Z_vs_SMC |
2
|
1.646
|
0.111
|
0.300
|
| DEMetro_Z_vs_SMC |
3
|
0.660
|
0.515
|
0.120
|
| DEMetro_Z_vs_SMC |
4
|
1.152
|
0.259
|
0.210
|
| DEMetro_Z_vs_SMC |
5
|
1.686
|
0.103
|
0.308
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
4.678 |
12.635 |
33.274 |
-0.239 |
| HMC |
4 |
4.973 |
9.021 |
17.702 |
-0.229 |
| HMC |
6 |
5.422 |
15.222 |
35.975 |
-0.272 |
| HMC |
8 |
4.518 |
5.811 |
10.534 |
-0.123 |
| HMC |
10 |
5.039 |
7.441 |
11.232 |
-0.214 |
| HMC |
12 |
5.723 |
72.267 |
371.333 |
-0.179 |
| SMC |
0 |
7.140 |
12.635 |
33.274 |
-0.165 |
| SMC |
4 |
8.133 |
9.021 |
17.702 |
-0.050 |
| SMC |
6 |
4.463 |
15.222 |
35.975 |
-0.299 |
| SMC |
8 |
4.141 |
5.811 |
10.534 |
-0.159 |
| SMC |
10 |
3.790 |
7.441 |
11.232 |
-0.325 |
| SMC |
12 |
5.571 |
72.267 |
371.333 |
-0.180 |
| Metro |
0 |
3.806 |
12.635 |
33.274 |
-0.265 |
| Metro |
4 |
4.344 |
9.021 |
17.702 |
-0.264 |
| Metro |
6 |
6.084 |
15.222 |
35.975 |
-0.254 |
| Metro |
8 |
4.326 |
5.811 |
10.534 |
-0.141 |
| Metro |
10 |
3.894 |
7.441 |
11.232 |
-0.316 |
| Metro |
12 |
6.599 |
72.267 |
371.333 |
-0.177 |
| DEMetro_Z |
0 |
5.509 |
12.635 |
33.274 |
-0.214 |
| DEMetro_Z |
4 |
4.858 |
9.021 |
17.702 |
-0.235 |
| DEMetro_Z |
6 |
5.413 |
15.222 |
35.975 |
-0.273 |
| DEMetro_Z |
8 |
4.526 |
5.811 |
10.534 |
-0.122 |
| DEMetro_Z |
10 |
4.533 |
7.441 |
11.232 |
-0.259 |
| DEMetro_Z |
12 |
7.105 |
72.267 |
371.333 |
-0.175 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
2.275 |
0.0266 |
0.594 |
| HMC |
4 |
3.169 |
0.00277 |
1.230 |
| HMC |
6 |
3.361 |
0.0016 |
1.295 |
| HMC |
8 |
6.230 |
4.1e-07 |
3.862 |
| HMC |
10 |
5.645 |
3.08e-06 |
4.748 |
| HMC |
12 |
6.674 |
1.01e-07 |
3.970 |
| SMC |
0 |
9.304 |
1.46e-10 |
8.206 |
| SMC |
4 |
9.158 |
1.72e-10 |
7.230 |
| SMC |
6 |
7.747 |
3.04e-09 |
4.075 |
| SMC |
8 |
9.615 |
2.76e-11 |
5.964 |
| SMC |
10 |
9.123 |
1.2e-10 |
5.958 |
| SMC |
12 |
7.425 |
4.23e-09 |
3.224 |
| Metro |
0 |
4.788 |
1.61e-05 |
1.647 |
| Metro |
4 |
5.969 |
4.58e-07 |
2.533 |
| Metro |
6 |
4.904 |
1.85e-05 |
2.498 |
| Metro |
8 |
6.749 |
2.71e-08 |
2.651 |
| Metro |
10 |
5.650 |
1.79e-06 |
2.854 |
| Metro |
12 |
6.022 |
1.66e-07 |
1.864 |
| DEMetro_Z |
0 |
9.778 |
5.07e-13 |
3.411 |
| DEMetro_Z |
4 |
10.233 |
7.89e-14 |
3.436 |
| DEMetro_Z |
6 |
8.326 |
6.17e-11 |
2.850 |
| DEMetro_Z |
8 |
6.707 |
1.67e-07 |
6.713 |
| DEMetro_Z |
10 |
7.246 |
3.94e-08 |
7.688 |
| DEMetro_Z |
12 |
7.404 |
1.42e-08 |
4.842 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-4.569
|
8.38e-05
|
-0.834
|
| Metro_vs_DEMetro_Z |
1
|
-2.128
|
0.0419
|
-0.389
|
| Metro_vs_DEMetro_Z |
2
|
-0.614
|
0.544
|
-0.112
|
| Metro_vs_DEMetro_Z |
3
|
-3.603
|
0.00116
|
-0.658
|
| Metro_vs_DEMetro_Z |
4
|
-4.156
|
0.000261
|
-0.759
|
| Metro_vs_DEMetro_Z |
5
|
-4.334
|
0.00016
|
-0.791
|
| DEMetro_Z_vs_SMC |
0
|
-5.298
|
1.11e-05
|
-0.967
|
| DEMetro_Z_vs_SMC |
1
|
-4.549
|
8.86e-05
|
-0.831
|
| DEMetro_Z_vs_SMC |
2
|
-2.046
|
0.05
|
-0.373
|
| DEMetro_Z_vs_SMC |
3
|
0.615
|
0.543
|
0.112
|
| DEMetro_Z_vs_SMC |
4
|
1.248
|
0.222
|
0.228
|
| DEMetro_Z_vs_SMC |
5
|
2.200
|
0.0359
|
0.402
|
| HMC_vs_DEMetro_Z |
0
|
-8.076
|
6.61e-09
|
-1.475
|
| HMC_vs_DEMetro_Z |
1
|
-5.374
|
8.97e-06
|
-0.981
|
| HMC_vs_DEMetro_Z |
2
|
-4.007
|
0.000392
|
-0.732
|
| HMC_vs_DEMetro_Z |
3
|
-2.560
|
0.0159
|
-0.467
|
| HMC_vs_DEMetro_Z |
4
|
-2.457
|
0.0202
|
-0.449
|
| HMC_vs_DEMetro_Z |
5
|
-1.114
|
0.274
|
-0.203
|
| HMC_vs_Metro |
0
|
-3.141
|
0.00385
|
-0.574
|
| HMC_vs_Metro |
1
|
-2.634
|
0.0134
|
-0.481
|
| HMC_vs_Metro |
2
|
-2.422
|
0.0219
|
-0.442
|
| HMC_vs_Metro |
3
|
1.459
|
0.155
|
0.266
|
| HMC_vs_Metro |
4
|
2.040
|
0.0506
|
0.372
|
| HMC_vs_Metro |
5
|
3.315
|
0.00247
|
0.605
|
| HMC_vs_SMC |
0
|
-9.005
|
6.73e-10
|
-1.644
|
| HMC_vs_SMC |
1
|
-7.134
|
7.5e-08
|
-1.303
|
| HMC_vs_SMC |
2
|
-4.913
|
3.23e-05
|
-0.897
|
| HMC_vs_SMC |
3
|
-2.429
|
0.0216
|
-0.444
|
| HMC_vs_SMC |
4
|
-1.192
|
0.243
|
-0.218
|
| HMC_vs_SMC |
5
|
1.055
|
0.3
|
0.193
|
| Metro_vs_SMC |
0
|
-7.317
|
4.65e-08
|
-1.336
|
| Metro_vs_SMC |
1
|
-5.877
|
2.23e-06
|
-1.073
|
| Metro_vs_SMC |
2
|
-2.268
|
0.0309
|
-0.414
|
| Metro_vs_SMC |
3
|
-4.577
|
8.2e-05
|
-0.836
|
| Metro_vs_SMC |
4
|
-3.940
|
0.000471
|
-0.719
|
| Metro_vs_SMC |
5
|
-2.941
|
0.00636
|
-0.537
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.149 |
0.123 |
0.044 |
0.594 |
| HMC |
4 |
0.179 |
0.130 |
0.040 |
1.230 |
| HMC |
6 |
0.217 |
0.156 |
0.048 |
1.295 |
| HMC |
8 |
0.299 |
0.145 |
0.040 |
3.862 |
| HMC |
10 |
0.388 |
0.159 |
0.048 |
4.748 |
| HMC |
12 |
0.592 |
0.168 |
0.107 |
3.970 |
| SMC |
0 |
0.481 |
0.123 |
0.044 |
8.206 |
| SMC |
4 |
0.417 |
0.130 |
0.040 |
7.230 |
| SMC |
6 |
0.349 |
0.156 |
0.048 |
4.075 |
| SMC |
8 |
0.382 |
0.145 |
0.040 |
5.964 |
| SMC |
10 |
0.447 |
0.159 |
0.048 |
5.958 |
| SMC |
12 |
0.512 |
0.168 |
0.107 |
3.224 |
| Metro |
0 |
0.195 |
0.123 |
0.044 |
1.647 |
| Metro |
4 |
0.230 |
0.130 |
0.040 |
2.533 |
| Metro |
6 |
0.274 |
0.156 |
0.048 |
2.498 |
| Metro |
8 |
0.250 |
0.145 |
0.040 |
2.651 |
| Metro |
10 |
0.297 |
0.159 |
0.048 |
2.854 |
| Metro |
12 |
0.367 |
0.168 |
0.107 |
1.864 |
| DEMetro_Z |
0 |
0.272 |
0.123 |
0.044 |
3.411 |
| DEMetro_Z |
4 |
0.266 |
0.130 |
0.040 |
3.436 |
| DEMetro_Z |
6 |
0.291 |
0.156 |
0.048 |
2.850 |
| DEMetro_Z |
8 |
0.412 |
0.145 |
0.040 |
6.713 |
| DEMetro_Z |
10 |
0.530 |
0.159 |
0.048 |
7.688 |
| DEMetro_Z |
12 |
0.685 |
0.168 |
0.107 |
4.842 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
3.233 |
0.00208 |
0.966 |
| HMC |
4 |
4.833 |
2.75e-05 |
3.003 |
| HMC |
6 |
4.258 |
0.00015 |
2.613 |
| HMC |
8 |
5.729 |
2.24e-06 |
4.329 |
| HMC |
10 |
5.507 |
5.31e-06 |
6.415 |
| HMC |
12 |
7.303 |
4.45e-08 |
16.621 |
| SMC |
0 |
11.812 |
9.23e-13 |
18.868 |
| SMC |
4 |
10.447 |
1.61e-11 |
14.392 |
| SMC |
6 |
7.072 |
5.49e-08 |
6.264 |
| SMC |
8 |
6.921 |
5.92e-08 |
4.613 |
| SMC |
10 |
6.140 |
7.26e-07 |
5.065 |
| SMC |
12 |
5.665 |
3.68e-06 |
9.359 |
| Metro |
0 |
7.670 |
1.65e-09 |
3.212 |
| Metro |
4 |
6.152 |
8.05e-07 |
6.284 |
| Metro |
6 |
6.027 |
3.69e-07 |
2.532 |
| Metro |
8 |
4.785 |
2.06e-05 |
1.947 |
| Metro |
10 |
5.127 |
1.02e-05 |
2.841 |
| Metro |
12 |
6.960 |
7.64e-08 |
6.297 |
| DEMetro_Z |
0 |
7.593 |
1.19e-08 |
6.232 |
| DEMetro_Z |
4 |
9.555 |
5.87e-11 |
7.314 |
| DEMetro_Z |
6 |
6.849 |
4.82e-08 |
3.665 |
| DEMetro_Z |
8 |
5.262 |
1.08e-05 |
6.495 |
| DEMetro_Z |
10 |
6.555 |
2.99e-07 |
9.166 |
| DEMetro_Z |
12 |
7.127 |
7.25e-08 |
19.058 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-6.558
|
3.49e-07
|
-1.197
|
| DEMetro_Z_vs_SMC |
1
|
-4.415
|
0.000128
|
-0.806
|
| DEMetro_Z_vs_SMC |
2
|
-2.522
|
0.0174
|
-0.461
|
| DEMetro_Z_vs_SMC |
3
|
1.340
|
0.191
|
0.245
|
| DEMetro_Z_vs_SMC |
4
|
2.207
|
0.0354
|
0.403
|
| DEMetro_Z_vs_SMC |
5
|
3.273
|
0.00275
|
0.598
|
| HMC_vs_Metro |
0
|
-5.050
|
2.21e-05
|
-0.922
|
| HMC_vs_Metro |
1
|
-3.672
|
0.000968
|
-0.670
|
| HMC_vs_Metro |
2
|
0.122
|
0.904
|
0.022
|
| HMC_vs_Metro |
3
|
2.441
|
0.021
|
0.446
|
| HMC_vs_Metro |
4
|
2.739
|
0.0104
|
0.500
|
| HMC_vs_Metro |
5
|
4.028
|
0.00037
|
0.735
|
| Metro_vs_DEMetro_Z |
0
|
-2.974
|
0.00587
|
-0.543
|
| Metro_vs_DEMetro_Z |
1
|
-0.757
|
0.455
|
-0.138
|
| Metro_vs_DEMetro_Z |
2
|
-1.647
|
0.11
|
-0.301
|
| Metro_vs_DEMetro_Z |
3
|
-3.375
|
0.00211
|
-0.616
|
| Metro_vs_DEMetro_Z |
4
|
-4.060
|
0.00034
|
-0.741
|
| Metro_vs_DEMetro_Z |
5
|
-4.397
|
0.000135
|
-0.803
|
| HMC_vs_SMC |
0
|
-11.627
|
1.94e-12
|
-2.123
|
| HMC_vs_SMC |
1
|
-7.445
|
3.32e-08
|
-1.359
|
| HMC_vs_SMC |
2
|
-3.914
|
0.000506
|
-0.715
|
| HMC_vs_SMC |
3
|
-0.263
|
0.795
|
-0.048
|
| HMC_vs_SMC |
4
|
0.996
|
0.328
|
0.182
|
| HMC_vs_SMC |
5
|
2.602
|
0.0144
|
0.475
|
| Metro_vs_SMC |
0
|
-10.018
|
6.33e-11
|
-1.829
|
| Metro_vs_SMC |
1
|
-4.832
|
4.05e-05
|
-0.882
|
| Metro_vs_SMC |
2
|
-4.178
|
0.000246
|
-0.763
|
| Metro_vs_SMC |
3
|
-3.610
|
0.00114
|
-0.659
|
| Metro_vs_SMC |
4
|
-2.073
|
0.0472
|
-0.378
|
| Metro_vs_SMC |
5
|
-1.555
|
0.131
|
-0.284
|
| HMC_vs_DEMetro_Z |
0
|
-6.200
|
9.21e-07
|
-1.132
|
| HMC_vs_DEMetro_Z |
1
|
-4.110
|
0.000297
|
-0.750
|
| HMC_vs_DEMetro_Z |
2
|
-1.382
|
0.178
|
-0.252
|
| HMC_vs_DEMetro_Z |
3
|
-1.572
|
0.127
|
-0.287
|
| HMC_vs_DEMetro_Z |
4
|
-1.747
|
0.0913
|
-0.319
|
| HMC_vs_DEMetro_Z |
5
|
-0.726
|
0.474
|
-0.133
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.019 |
0.015 |
0.004 |
0.966 |
| HMC |
4 |
0.022 |
0.012 |
0.003 |
3.003 |
| HMC |
6 |
0.029 |
0.014 |
0.006 |
2.613 |
| HMC |
8 |
0.041 |
0.013 |
0.006 |
4.329 |
| HMC |
10 |
0.051 |
0.012 |
0.006 |
6.415 |
| HMC |
12 |
0.069 |
0.010 |
0.004 |
16.621 |
| SMC |
0 |
0.096 |
0.015 |
0.004 |
18.868 |
| SMC |
4 |
0.058 |
0.012 |
0.003 |
14.392 |
| SMC |
6 |
0.050 |
0.014 |
0.006 |
6.264 |
| SMC |
8 |
0.043 |
0.013 |
0.006 |
4.613 |
| SMC |
10 |
0.043 |
0.012 |
0.006 |
5.065 |
| SMC |
12 |
0.043 |
0.010 |
0.004 |
9.359 |
| Metro |
0 |
0.029 |
0.015 |
0.004 |
3.212 |
| Metro |
4 |
0.032 |
0.012 |
0.003 |
6.284 |
| Metro |
6 |
0.029 |
0.014 |
0.006 |
2.532 |
| Metro |
8 |
0.026 |
0.013 |
0.006 |
1.947 |
| Metro |
10 |
0.029 |
0.012 |
0.006 |
2.841 |
| Metro |
12 |
0.032 |
0.010 |
0.004 |
6.297 |
| DEMetro_Z |
0 |
0.042 |
0.015 |
0.004 |
6.232 |
| DEMetro_Z |
4 |
0.036 |
0.012 |
0.003 |
7.314 |
| DEMetro_Z |
6 |
0.035 |
0.014 |
0.006 |
3.665 |
| DEMetro_Z |
8 |
0.055 |
0.013 |
0.006 |
6.495 |
| DEMetro_Z |
10 |
0.067 |
0.012 |
0.006 |
9.166 |
| DEMetro_Z |
12 |
0.078 |
0.010 |
0.004 |
19.058 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
1.791 |
0.0801 |
0.704 |
| HMC |
4 |
3.146 |
0.00316 |
1.483 |
| HMC |
6 |
3.472 |
0.00107 |
1.149 |
| HMC |
8 |
5.338 |
3.35e-06 |
2.163 |
| HMC |
10 |
4.226 |
0.000176 |
3.011 |
| HMC |
12 |
6.793 |
6.42e-08 |
3.837 |
| SMC |
0 |
1.577 |
0.121 |
0.490 |
| SMC |
4 |
3.236 |
0.00262 |
1.839 |
| SMC |
6 |
2.155 |
0.0368 |
0.870 |
| SMC |
8 |
4.025 |
0.000239 |
1.733 |
| SMC |
10 |
4.749 |
3.85e-05 |
3.396 |
| SMC |
12 |
6.436 |
8.93e-08 |
2.642 |
| Metro |
0 |
2.894 |
0.00665 |
1.979 |
| Metro |
4 |
3.468 |
0.00145 |
2.326 |
| Metro |
6 |
3.746 |
0.000607 |
1.925 |
| Metro |
8 |
4.147 |
0.000188 |
2.132 |
| Metro |
10 |
4.062 |
0.000256 |
2.321 |
| Metro |
12 |
3.842 |
0.000414 |
1.646 |
| DEMetro_Z |
0 |
3.908 |
0.000462 |
3.511 |
| DEMetro_Z |
4 |
5.110 |
1.48e-05 |
4.422 |
| DEMetro_Z |
6 |
4.649 |
3.75e-05 |
2.173 |
| DEMetro_Z |
8 |
3.716 |
0.000739 |
2.552 |
| DEMetro_Z |
10 |
5.380 |
5.99e-06 |
3.840 |
| DEMetro_Z |
12 |
6.243 |
4.29e-07 |
4.119 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.350
|
0.00225
|
-0.612
|
| HMC_vs_DEMetro_Z |
1
|
-2.744
|
0.0103
|
-0.501
|
| HMC_vs_DEMetro_Z |
2
|
-1.859
|
0.0732
|
-0.339
|
| HMC_vs_DEMetro_Z |
3
|
-0.503
|
0.619
|
-0.092
|
| HMC_vs_DEMetro_Z |
4
|
-0.862
|
0.396
|
-0.157
|
| HMC_vs_DEMetro_Z |
5
|
-0.356
|
0.725
|
-0.065
|
| Metro_vs_SMC |
0
|
2.424
|
0.0218
|
0.443
|
| Metro_vs_SMC |
1
|
0.757
|
0.455
|
0.138
|
| Metro_vs_SMC |
2
|
1.792
|
0.0835
|
0.327
|
| Metro_vs_SMC |
3
|
0.646
|
0.523
|
0.118
|
| Metro_vs_SMC |
4
|
-1.358
|
0.185
|
-0.248
|
| Metro_vs_SMC |
5
|
-1.819
|
0.0793
|
-0.332
|
| Metro_vs_DEMetro_Z |
0
|
-1.264
|
0.216
|
-0.231
|
| Metro_vs_DEMetro_Z |
1
|
-1.850
|
0.0746
|
-0.338
|
| Metro_vs_DEMetro_Z |
2
|
-0.417
|
0.68
|
-0.076
|
| Metro_vs_DEMetro_Z |
3
|
-0.508
|
0.615
|
-0.093
|
| Metro_vs_DEMetro_Z |
4
|
-1.720
|
0.0961
|
-0.314
|
| Metro_vs_DEMetro_Z |
5
|
-3.104
|
0.00423
|
-0.567
|
| HMC_vs_Metro |
0
|
-1.663
|
0.107
|
-0.304
|
| HMC_vs_Metro |
1
|
-0.967
|
0.341
|
-0.177
|
| HMC_vs_Metro |
2
|
-1.427
|
0.164
|
-0.261
|
| HMC_vs_Metro |
3
|
0.054
|
0.958
|
0.010
|
| HMC_vs_Metro |
4
|
0.762
|
0.452
|
0.139
|
| HMC_vs_Metro |
5
|
3.057
|
0.00477
|
0.558
|
| HMC_vs_SMC |
0
|
0.499
|
0.622
|
0.091
|
| HMC_vs_SMC |
1
|
-0.489
|
0.629
|
-0.089
|
| HMC_vs_SMC |
2
|
0.618
|
0.541
|
0.113
|
| HMC_vs_SMC |
3
|
0.816
|
0.421
|
0.149
|
| HMC_vs_SMC |
4
|
-0.381
|
0.706
|
-0.070
|
| HMC_vs_SMC |
5
|
1.613
|
0.118
|
0.294
|
| DEMetro_Z_vs_SMC |
0
|
3.258
|
0.00286
|
0.595
|
| DEMetro_Z_vs_SMC |
1
|
2.475
|
0.0194
|
0.452
|
| DEMetro_Z_vs_SMC |
2
|
2.508
|
0.018
|
0.458
|
| DEMetro_Z_vs_SMC |
3
|
1.267
|
0.215
|
0.231
|
| DEMetro_Z_vs_SMC |
4
|
0.409
|
0.686
|
0.075
|
| DEMetro_Z_vs_SMC |
5
|
1.859
|
0.0731
|
0.339
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.078 |
0.056 |
0.031 |
0.704 |
| HMC |
4 |
0.095 |
0.056 |
0.026 |
1.483 |
| HMC |
6 |
0.143 |
0.084 |
0.051 |
1.149 |
| HMC |
8 |
0.206 |
0.080 |
0.058 |
2.163 |
| HMC |
10 |
0.261 |
0.096 |
0.055 |
3.011 |
| HMC |
12 |
0.504 |
0.091 |
0.108 |
3.837 |
| SMC |
0 |
0.071 |
0.056 |
0.031 |
0.490 |
| SMC |
4 |
0.104 |
0.056 |
0.026 |
1.839 |
| SMC |
6 |
0.129 |
0.084 |
0.051 |
0.870 |
| SMC |
8 |
0.181 |
0.080 |
0.058 |
1.733 |
| SMC |
10 |
0.282 |
0.096 |
0.055 |
3.396 |
| SMC |
12 |
0.375 |
0.091 |
0.108 |
2.642 |
| Metro |
0 |
0.117 |
0.056 |
0.031 |
1.979 |
| Metro |
4 |
0.116 |
0.056 |
0.026 |
2.326 |
| Metro |
6 |
0.183 |
0.084 |
0.051 |
1.925 |
| Metro |
8 |
0.204 |
0.080 |
0.058 |
2.132 |
| Metro |
10 |
0.223 |
0.096 |
0.055 |
2.321 |
| Metro |
12 |
0.268 |
0.091 |
0.108 |
1.646 |
| DEMetro_Z |
0 |
0.164 |
0.056 |
0.031 |
3.511 |
| DEMetro_Z |
4 |
0.170 |
0.056 |
0.026 |
4.422 |
| DEMetro_Z |
6 |
0.195 |
0.084 |
0.051 |
2.173 |
| DEMetro_Z |
8 |
0.228 |
0.080 |
0.058 |
2.552 |
| DEMetro_Z |
10 |
0.306 |
0.096 |
0.055 |
3.840 |
| DEMetro_Z |
12 |
0.534 |
0.091 |
0.108 |
4.119 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
-0.601 |
0.55 |
-0.130 |
| HMC |
4 |
-0.835 |
0.408 |
-0.170 |
| HMC |
6 |
-0.945 |
0.351 |
-0.187 |
| HMC |
8 |
-0.817 |
0.419 |
-0.164 |
| HMC |
10 |
-1.167 |
0.25 |
-0.242 |
| HMC |
12 |
-0.968 |
0.341 |
-0.177 |
| SMC |
0 |
-1.339 |
0.191 |
-0.246 |
| SMC |
4 |
-1.178 |
0.248 |
-0.219 |
| SMC |
6 |
-1.778 |
0.0858 |
-0.326 |
| SMC |
8 |
-1.104 |
0.276 |
-0.217 |
| SMC |
10 |
-1.781 |
0.0839 |
-0.338 |
| SMC |
12 |
-0.982 |
0.334 |
-0.179 |
| Metro |
0 |
-1.101 |
0.279 |
-0.207 |
| Metro |
4 |
-1.518 |
0.139 |
-0.284 |
| Metro |
6 |
-1.300 |
0.203 |
-0.241 |
| Metro |
8 |
-0.367 |
0.715 |
-0.081 |
| Metro |
10 |
-1.201 |
0.238 |
-0.232 |
| Metro |
12 |
-0.923 |
0.364 |
-0.169 |
| DEMetro_Z |
0 |
-1.136 |
0.265 |
-0.211 |
| DEMetro_Z |
4 |
-1.464 |
0.154 |
-0.271 |
| DEMetro_Z |
6 |
-1.356 |
0.185 |
-0.250 |
| DEMetro_Z |
8 |
-0.401 |
0.691 |
-0.082 |
| DEMetro_Z |
10 |
-1.582 |
0.123 |
-0.297 |
| DEMetro_Z |
12 |
-0.961 |
0.345 |
-0.175 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.991
|
0.33
|
0.181
|
| HMC_vs_SMC |
1
|
0.524
|
0.604
|
0.096
|
| HMC_vs_SMC |
2
|
1.795
|
0.0831
|
0.328
|
| HMC_vs_SMC |
3
|
1.080
|
0.289
|
0.197
|
| HMC_vs_SMC |
4
|
0.897
|
0.377
|
0.164
|
| HMC_vs_SMC |
5
|
2.221
|
0.0344
|
0.405
|
| Metro_vs_DEMetro_Z |
0
|
0.092
|
0.928
|
0.017
|
| Metro_vs_DEMetro_Z |
1
|
-0.735
|
0.468
|
-0.134
|
| Metro_vs_DEMetro_Z |
2
|
0.298
|
0.768
|
0.054
|
| Metro_vs_DEMetro_Z |
3
|
0.011
|
0.992
|
0.002
|
| Metro_vs_DEMetro_Z |
4
|
1.091
|
0.284
|
0.199
|
| Metro_vs_DEMetro_Z |
5
|
0.835
|
0.411
|
0.152
|
| HMC_vs_Metro |
0
|
0.640
|
0.528
|
0.117
|
| HMC_vs_Metro |
1
|
1.408
|
0.17
|
0.257
|
| HMC_vs_Metro |
2
|
0.657
|
0.516
|
0.120
|
| HMC_vs_Metro |
3
|
-0.744
|
0.463
|
-0.136
|
| HMC_vs_Metro |
4
|
-0.090
|
0.929
|
-0.016
|
| HMC_vs_Metro |
5
|
-1.013
|
0.319
|
-0.185
|
| HMC_vs_DEMetro_Z |
0
|
0.686
|
0.498
|
0.125
|
| HMC_vs_DEMetro_Z |
1
|
1.232
|
0.228
|
0.225
|
| HMC_vs_DEMetro_Z |
2
|
0.772
|
0.446
|
0.141
|
| HMC_vs_DEMetro_Z |
3
|
-1.283
|
0.21
|
-0.234
|
| HMC_vs_DEMetro_Z |
4
|
0.615
|
0.543
|
0.112
|
| HMC_vs_DEMetro_Z |
5
|
-0.884
|
0.384
|
-0.161
|
| Metro_vs_SMC |
0
|
0.856
|
0.399
|
0.156
|
| Metro_vs_SMC |
1
|
-1.360
|
0.184
|
-0.248
|
| Metro_vs_SMC |
2
|
3.425
|
0.00186
|
0.625
|
| Metro_vs_SMC |
3
|
1.623
|
0.115
|
0.296
|
| Metro_vs_SMC |
4
|
1.779
|
0.0857
|
0.325
|
| Metro_vs_SMC |
5
|
1.336
|
0.192
|
0.244
|
| DEMetro_Z_vs_SMC |
0
|
1.020
|
0.316
|
0.186
|
| DEMetro_Z_vs_SMC |
1
|
-1.174
|
0.25
|
-0.214
|
| DEMetro_Z_vs_SMC |
2
|
4.219
|
0.00022
|
0.770
|
| DEMetro_Z_vs_SMC |
3
|
2.511
|
0.0179
|
0.458
|
| DEMetro_Z_vs_SMC |
4
|
0.836
|
0.41
|
0.153
|
| DEMetro_Z_vs_SMC |
5
|
3.097
|
0.00431
|
0.565
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
8.321 |
12.635 |
33.274 |
-0.130 |
| HMC |
4 |
6.020 |
9.021 |
17.702 |
-0.170 |
| HMC |
6 |
8.486 |
15.222 |
35.975 |
-0.187 |
| HMC |
8 |
4.085 |
5.811 |
10.534 |
-0.164 |
| HMC |
10 |
4.727 |
7.441 |
11.232 |
-0.242 |
| HMC |
12 |
6.639 |
72.267 |
371.333 |
-0.177 |
| SMC |
0 |
4.443 |
12.635 |
33.274 |
-0.246 |
| SMC |
4 |
5.137 |
9.021 |
17.702 |
-0.219 |
| SMC |
6 |
3.503 |
15.222 |
35.975 |
-0.326 |
| SMC |
8 |
3.521 |
5.811 |
10.534 |
-0.217 |
| SMC |
10 |
3.640 |
7.441 |
11.232 |
-0.338 |
| SMC |
12 |
5.689 |
72.267 |
371.333 |
-0.179 |
| Metro |
0 |
5.759 |
12.635 |
33.274 |
-0.207 |
| Metro |
4 |
4.000 |
9.021 |
17.702 |
-0.284 |
| Metro |
6 |
6.560 |
15.222 |
35.975 |
-0.241 |
| Metro |
8 |
4.958 |
5.811 |
10.534 |
-0.081 |
| Metro |
10 |
4.839 |
7.441 |
11.232 |
-0.232 |
| Metro |
12 |
9.634 |
72.267 |
371.333 |
-0.169 |
| DEMetro_Z |
0 |
5.609 |
12.635 |
33.274 |
-0.211 |
| DEMetro_Z |
4 |
4.227 |
9.021 |
17.702 |
-0.271 |
| DEMetro_Z |
6 |
6.244 |
15.222 |
35.975 |
-0.250 |
| DEMetro_Z |
8 |
4.948 |
5.811 |
10.534 |
-0.082 |
| DEMetro_Z |
10 |
4.101 |
7.441 |
11.232 |
-0.297 |
| DEMetro_Z |
12 |
7.136 |
72.267 |
371.333 |
-0.175 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
2.933 |
0.00538 |
1.198 |
| HMC |
4 |
3.713 |
0.000557 |
1.388 |
| HMC |
6 |
4.712 |
2.36e-05 |
1.776 |
| HMC |
8 |
5.847 |
1.14e-06 |
3.296 |
| HMC |
10 |
5.220 |
9.47e-06 |
3.647 |
| HMC |
12 |
6.805 |
5.48e-08 |
3.630 |
| SMC |
0 |
5.081 |
1.6e-05 |
4.366 |
| SMC |
4 |
5.767 |
1.77e-06 |
3.799 |
| SMC |
6 |
3.892 |
0.000352 |
1.645 |
| SMC |
8 |
6.805 |
5.83e-08 |
3.732 |
| SMC |
10 |
6.318 |
4e-07 |
4.757 |
| SMC |
12 |
6.841 |
1.86e-08 |
2.640 |
| Metro |
0 |
5.231 |
5.72e-06 |
2.373 |
| Metro |
4 |
4.941 |
1.11e-05 |
1.863 |
| Metro |
6 |
5.175 |
7.58e-06 |
2.523 |
| Metro |
8 |
5.622 |
2.5e-06 |
3.420 |
| Metro |
10 |
6.217 |
3.53e-07 |
3.413 |
| Metro |
12 |
3.956 |
0.000315 |
1.877 |
| DEMetro_Z |
0 |
7.338 |
8.92e-09 |
3.657 |
| DEMetro_Z |
4 |
7.264 |
1.43e-08 |
3.953 |
| DEMetro_Z |
6 |
9.507 |
2.36e-12 |
3.589 |
| DEMetro_Z |
8 |
5.439 |
5.8e-06 |
4.884 |
| DEMetro_Z |
10 |
7.968 |
3.26e-09 |
5.557 |
| DEMetro_Z |
12 |
7.044 |
3.43e-08 |
4.229 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.106
|
0.044
|
-0.384
|
| Metro_vs_DEMetro_Z |
1
|
-3.710
|
0.000873
|
-0.677
|
| Metro_vs_DEMetro_Z |
2
|
-2.103
|
0.0442
|
-0.384
|
| Metro_vs_DEMetro_Z |
3
|
-1.543
|
0.134
|
-0.282
|
| Metro_vs_DEMetro_Z |
4
|
-2.465
|
0.0198
|
-0.450
|
| Metro_vs_DEMetro_Z |
5
|
-3.095
|
0.00434
|
-0.565
|
| DEMetro_Z_vs_SMC |
0
|
-0.824
|
0.417
|
-0.150
|
| DEMetro_Z_vs_SMC |
1
|
0.169
|
0.867
|
0.031
|
| DEMetro_Z_vs_SMC |
2
|
4.568
|
8.41e-05
|
0.834
|
| DEMetro_Z_vs_SMC |
3
|
1.541
|
0.134
|
0.281
|
| DEMetro_Z_vs_SMC |
4
|
0.714
|
0.481
|
0.130
|
| DEMetro_Z_vs_SMC |
5
|
2.140
|
0.0409
|
0.391
|
| HMC_vs_DEMetro_Z |
0
|
-4.495
|
0.000103
|
-0.821
|
| HMC_vs_DEMetro_Z |
1
|
-4.060
|
0.00034
|
-0.741
|
| HMC_vs_DEMetro_Z |
2
|
-3.666
|
0.000983
|
-0.669
|
| HMC_vs_DEMetro_Z |
3
|
-1.505
|
0.143
|
-0.275
|
| HMC_vs_DEMetro_Z |
4
|
-2.171
|
0.0383
|
-0.396
|
| HMC_vs_DEMetro_Z |
5
|
-0.831
|
0.413
|
-0.152
|
| HMC_vs_Metro |
0
|
-2.116
|
0.0431
|
-0.386
|
| HMC_vs_Metro |
1
|
-0.965
|
0.343
|
-0.176
|
| HMC_vs_Metro |
2
|
-1.217
|
0.233
|
-0.222
|
| HMC_vs_Metro |
3
|
-0.158
|
0.875
|
-0.029
|
| HMC_vs_Metro |
4
|
0.283
|
0.779
|
0.052
|
| HMC_vs_Metro |
5
|
2.466
|
0.0198
|
0.450
|
| HMC_vs_SMC |
0
|
-3.350
|
0.00226
|
-0.612
|
| HMC_vs_SMC |
1
|
-3.032
|
0.00508
|
-0.554
|
| HMC_vs_SMC |
2
|
0.251
|
0.804
|
0.046
|
| HMC_vs_SMC |
3
|
-0.589
|
0.56
|
-0.108
|
| HMC_vs_SMC |
4
|
-1.135
|
0.266
|
-0.207
|
| HMC_vs_SMC |
5
|
1.452
|
0.157
|
0.265
|
| Metro_vs_SMC |
0
|
-2.116
|
0.043
|
-0.386
|
| Metro_vs_SMC |
1
|
-2.675
|
0.0121
|
-0.488
|
| Metro_vs_SMC |
2
|
1.590
|
0.123
|
0.290
|
| Metro_vs_SMC |
3
|
-0.467
|
0.644
|
-0.085
|
| Metro_vs_SMC |
4
|
-1.590
|
0.123
|
-0.290
|
| Metro_vs_SMC |
5
|
-1.322
|
0.197
|
-0.241
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.175 |
0.123 |
0.044 |
1.198 |
| HMC |
4 |
0.185 |
0.130 |
0.040 |
1.388 |
| HMC |
6 |
0.240 |
0.156 |
0.048 |
1.776 |
| HMC |
8 |
0.276 |
0.145 |
0.040 |
3.296 |
| HMC |
10 |
0.335 |
0.159 |
0.048 |
3.647 |
| HMC |
12 |
0.556 |
0.168 |
0.107 |
3.630 |
| SMC |
0 |
0.313 |
0.123 |
0.044 |
4.366 |
| SMC |
4 |
0.281 |
0.130 |
0.040 |
3.799 |
| SMC |
6 |
0.234 |
0.156 |
0.048 |
1.645 |
| SMC |
8 |
0.293 |
0.145 |
0.040 |
3.732 |
| SMC |
10 |
0.389 |
0.159 |
0.048 |
4.757 |
| SMC |
12 |
0.450 |
0.168 |
0.107 |
2.640 |
| Metro |
0 |
0.226 |
0.123 |
0.044 |
2.373 |
| Metro |
4 |
0.204 |
0.130 |
0.040 |
1.863 |
| Metro |
6 |
0.275 |
0.156 |
0.048 |
2.523 |
| Metro |
8 |
0.281 |
0.145 |
0.040 |
3.420 |
| Metro |
10 |
0.324 |
0.159 |
0.048 |
3.413 |
| Metro |
12 |
0.369 |
0.168 |
0.107 |
1.877 |
| DEMetro_Z |
0 |
0.282 |
0.123 |
0.044 |
3.657 |
| DEMetro_Z |
4 |
0.287 |
0.130 |
0.040 |
3.953 |
| DEMetro_Z |
6 |
0.326 |
0.156 |
0.048 |
3.589 |
| DEMetro_Z |
8 |
0.339 |
0.145 |
0.040 |
4.884 |
| DEMetro_Z |
10 |
0.427 |
0.159 |
0.048 |
5.557 |
| DEMetro_Z |
12 |
0.620 |
0.168 |
0.107 |
4.229 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0 |
2.775 |
0.00907 |
2.072 |
| HMC |
4 |
5.489 |
3.32e-06 |
3.010 |
| HMC |
6 |
4.321 |
0.00012 |
2.468 |
| HMC |
8 |
5.573 |
3.03e-06 |
3.528 |
| HMC |
10 |
4.783 |
3.96e-05 |
4.644 |
| HMC |
12 |
7.235 |
5.26e-08 |
15.288 |
| SMC |
0 |
6.839 |
1.45e-07 |
11.651 |
| SMC |
4 |
7.655 |
1.45e-08 |
9.538 |
| SMC |
6 |
4.600 |
5.68e-05 |
3.007 |
| SMC |
8 |
5.340 |
6.29e-06 |
3.495 |
| SMC |
10 |
5.575 |
4.03e-06 |
5.259 |
| SMC |
12 |
7.631 |
1.65e-08 |
10.772 |
| Metro |
0 |
8.397 |
4.26e-10 |
4.362 |
| Metro |
4 |
8.392 |
6.2e-10 |
4.846 |
| Metro |
6 |
5.334 |
3.21e-06 |
2.097 |
| Metro |
8 |
4.628 |
4.4e-05 |
2.391 |
| Metro |
10 |
6.135 |
3.77e-07 |
3.044 |
| Metro |
12 |
6.444 |
2.66e-07 |
4.664 |
| DEMetro_Z |
0 |
9.820 |
1.02e-11 |
5.438 |
| DEMetro_Z |
4 |
7.443 |
2.1e-08 |
7.067 |
| DEMetro_Z |
6 |
8.308 |
4.91e-10 |
4.183 |
| DEMetro_Z |
8 |
3.971 |
0.000394 |
3.835 |
| DEMetro_Z |
10 |
6.482 |
3e-07 |
6.058 |
| DEMetro_Z |
12 |
6.138 |
1.05e-06 |
16.587 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-3.649
|
0.00103
|
-0.666
|
| DEMetro_Z_vs_SMC |
1
|
-1.452
|
0.157
|
-0.265
|
| DEMetro_Z_vs_SMC |
2
|
1.811
|
0.0804
|
0.331
|
| DEMetro_Z_vs_SMC |
3
|
0.327
|
0.746
|
0.060
|
| DEMetro_Z_vs_SMC |
4
|
0.553
|
0.584
|
0.101
|
| DEMetro_Z_vs_SMC |
5
|
1.742
|
0.0921
|
0.318
|
| HMC_vs_Metro |
0
|
-2.732
|
0.0106
|
-0.499
|
| HMC_vs_Metro |
1
|
-2.496
|
0.0185
|
-0.456
|
| HMC_vs_Metro |
2
|
0.512
|
0.613
|
0.093
|
| HMC_vs_Metro |
3
|
1.401
|
0.172
|
0.256
|
| HMC_vs_Metro |
4
|
1.525
|
0.138
|
0.278
|
| HMC_vs_Metro |
5
|
4.526
|
9.44e-05
|
0.826
|
| Metro_vs_DEMetro_Z |
0
|
-1.396
|
0.173
|
-0.255
|
| Metro_vs_DEMetro_Z |
1
|
-1.979
|
0.0574
|
-0.361
|
| Metro_vs_DEMetro_Z |
2
|
-3.969
|
0.000435
|
-0.725
|
| Metro_vs_DEMetro_Z |
3
|
-1.355
|
0.186
|
-0.247
|
| Metro_vs_DEMetro_Z |
4
|
-3.185
|
0.00345
|
-0.582
|
| Metro_vs_DEMetro_Z |
5
|
-4.086
|
0.000316
|
-0.746
|
| HMC_vs_SMC |
0
|
-5.424
|
7.81e-06
|
-0.990
|
| HMC_vs_SMC |
1
|
-4.930
|
3.08e-05
|
-0.900
|
| HMC_vs_SMC |
2
|
-0.644
|
0.525
|
-0.118
|
| HMC_vs_SMC |
3
|
0.035
|
0.972
|
0.006
|
| HMC_vs_SMC |
4
|
-0.429
|
0.671
|
-0.078
|
| HMC_vs_SMC |
5
|
1.577
|
0.126
|
0.288
|
| Metro_vs_SMC |
0
|
-4.112
|
0.000295
|
-0.751
|
| Metro_vs_SMC |
1
|
-3.704
|
0.000889
|
-0.676
|
| Metro_vs_SMC |
2
|
-1.388
|
0.176
|
-0.253
|
| Metro_vs_SMC |
3
|
-1.466
|
0.153
|
-0.268
|
| Metro_vs_SMC |
4
|
-2.136
|
0.0412
|
-0.390
|
| Metro_vs_SMC |
5
|
-4.063
|
0.000337
|
-0.742
|
| HMC_vs_DEMetro_Z |
0
|
-3.443
|
0.00177
|
-0.629
|
| HMC_vs_DEMetro_Z |
1
|
-3.654
|
0.00101
|
-0.667
|
| HMC_vs_DEMetro_Z |
2
|
-2.432
|
0.0214
|
-0.444
|
| HMC_vs_DEMetro_Z |
3
|
-0.271
|
0.789
|
-0.049
|
| HMC_vs_DEMetro_Z |
4
|
-1.115
|
0.274
|
-0.204
|
| HMC_vs_DEMetro_Z |
5
|
-0.404
|
0.689
|
-0.074
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0 |
0.024 |
0.015 |
0.004 |
2.072 |
| HMC |
4 |
0.022 |
0.012 |
0.003 |
3.010 |
| HMC |
6 |
0.028 |
0.014 |
0.006 |
2.468 |
| HMC |
8 |
0.036 |
0.013 |
0.006 |
3.528 |
| HMC |
10 |
0.040 |
0.012 |
0.006 |
4.644 |
| HMC |
12 |
0.065 |
0.010 |
0.004 |
15.288 |
| SMC |
0 |
0.065 |
0.015 |
0.004 |
11.651 |
| SMC |
4 |
0.043 |
0.012 |
0.003 |
9.538 |
| SMC |
6 |
0.031 |
0.014 |
0.006 |
3.007 |
| SMC |
8 |
0.036 |
0.013 |
0.006 |
3.495 |
| SMC |
10 |
0.044 |
0.012 |
0.006 |
5.259 |
| SMC |
12 |
0.048 |
0.010 |
0.004 |
10.772 |
| Metro |
0 |
0.034 |
0.015 |
0.004 |
4.362 |
| Metro |
4 |
0.028 |
0.012 |
0.003 |
4.846 |
| Metro |
6 |
0.026 |
0.014 |
0.006 |
2.097 |
| Metro |
8 |
0.028 |
0.013 |
0.006 |
2.391 |
| Metro |
10 |
0.031 |
0.012 |
0.006 |
3.044 |
| Metro |
12 |
0.026 |
0.010 |
0.004 |
4.664 |
| DEMetro_Z |
0 |
0.038 |
0.015 |
0.004 |
5.438 |
| DEMetro_Z |
4 |
0.035 |
0.012 |
0.003 |
7.067 |
| DEMetro_Z |
6 |
0.038 |
0.014 |
0.006 |
4.183 |
| DEMetro_Z |
8 |
0.038 |
0.013 |
0.006 |
3.835 |
| DEMetro_Z |
10 |
0.049 |
0.012 |
0.006 |
6.058 |
| DEMetro_Z |
12 |
0.069 |
0.010 |
0.004 |
16.587 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Dimension
(MvStudentT,
nu,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.232 |
0.0333 |
3.525 |
| HMC |
2.5 |
2.524 |
0.017 |
2.606 |
| HMC |
3.0 |
2.280 |
0.03 |
3.771 |
| HMC |
4.0 |
0.994 |
0.328 |
0.809 |
| HMC |
10.0 |
-2.533 |
0.0141 |
-0.675 |
| HMC |
50.0 |
-5.996 |
1.43e-07 |
-1.478 |
| SMC |
2.1 |
20.634 |
7.62e-28 |
5.916 |
| SMC |
2.5 |
28.810 |
7.72e-26 |
17.450 |
| SMC |
3.0 |
30.967 |
1.88e-25 |
25.278 |
| SMC |
4.0 |
33.603 |
7.19e-26 |
34.797 |
| SMC |
10.0 |
36.157 |
3.38e-27 |
32.675 |
| SMC |
50.0 |
15.742 |
3.27e-20 |
5.764 |
| Metro |
2.1 |
6.788 |
1.72e-07 |
13.232 |
| Metro |
2.5 |
7.176 |
5.74e-08 |
11.191 |
| Metro |
3.0 |
11.079 |
1.3e-12 |
8.217 |
| Metro |
4.0 |
4.961 |
2.69e-05 |
9.045 |
| Metro |
10.0 |
16.404 |
7.66e-18 |
10.199 |
| Metro |
50.0 |
17.607 |
9.3e-20 |
8.846 |
| DEMetro_Z |
2.1 |
27.477 |
2.55e-22 |
353.621 |
| DEMetro_Z |
2.5 |
22.298 |
8.42e-20 |
497.613 |
| DEMetro_Z |
3.0 |
22.965 |
3.73e-20 |
357.048 |
| DEMetro_Z |
4.0 |
22.081 |
1.09e-19 |
295.679 |
| DEMetro_Z |
10.0 |
27.094 |
3.78e-22 |
380.531 |
| DEMetro_Z |
50.0 |
14.460 |
8.6e-15 |
342.419 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-28.777
|
7.07e-23
|
-5.254
|
| HMC_vs_DEMetro_Z |
1
|
-22.249
|
8.97e-20
|
-4.062
|
| HMC_vs_DEMetro_Z |
2
|
-22.196
|
9.57e-20
|
-4.052
|
| HMC_vs_DEMetro_Z |
3
|
-22.601
|
5.83e-20
|
-4.126
|
| HMC_vs_DEMetro_Z |
4
|
-27.046
|
4.02e-22
|
-4.938
|
| HMC_vs_DEMetro_Z |
5
|
-14.506
|
7.94e-15
|
-2.648
|
| Metro_vs_SMC |
0
|
3.778
|
0.000729
|
0.690
|
| Metro_vs_SMC |
1
|
-3.612
|
0.00113
|
-0.659
|
| Metro_vs_SMC |
2
|
-15.562
|
1.3e-15
|
-2.841
|
| Metro_vs_SMC |
3
|
-10.920
|
8.64e-12
|
-1.994
|
| Metro_vs_SMC |
4
|
-20.660
|
6.8e-19
|
-3.772
|
| Metro_vs_SMC |
5
|
5.543
|
5.61e-06
|
1.012
|
| Metro_vs_DEMetro_Z |
0
|
-25.603
|
1.85e-21
|
-4.674
|
| Metro_vs_DEMetro_Z |
1
|
-21.906
|
1.37e-19
|
-3.999
|
| Metro_vs_DEMetro_Z |
2
|
-22.210
|
9.42e-20
|
-4.055
|
| Metro_vs_DEMetro_Z |
3
|
-21.643
|
1.91e-19
|
-3.951
|
| Metro_vs_DEMetro_Z |
4
|
-26.634
|
6.16e-22
|
-4.863
|
| Metro_vs_DEMetro_Z |
5
|
-14.060
|
1.76e-14
|
-2.567
|
| HMC_vs_Metro |
0
|
-3.536
|
0.00139
|
-0.646
|
| HMC_vs_Metro |
1
|
-4.558
|
8.64e-05
|
-0.832
|
| HMC_vs_Metro |
2
|
-2.418
|
0.0221
|
-0.441
|
| HMC_vs_Metro |
3
|
-4.248
|
0.000203
|
-0.776
|
| HMC_vs_Metro |
4
|
-16.742
|
1.91e-16
|
-3.057
|
| HMC_vs_Metro |
5
|
-20.245
|
1.18e-18
|
-3.696
|
| HMC_vs_SMC |
0
|
-1.463
|
0.154
|
-0.267
|
| HMC_vs_SMC |
1
|
-12.083
|
7.67e-13
|
-2.206
|
| HMC_vs_SMC |
2
|
-11.971
|
9.61e-13
|
-2.186
|
| HMC_vs_SMC |
3
|
-26.740
|
5.52e-22
|
-4.882
|
| HMC_vs_SMC |
4
|
-39.618
|
8.34e-27
|
-7.233
|
| HMC_vs_SMC |
5
|
-19.402
|
3.73e-18
|
-3.542
|
| DEMetro_Z_vs_SMC |
0
|
26.935
|
4.5e-22
|
4.918
|
| DEMetro_Z_vs_SMC |
1
|
21.826
|
1.52e-19
|
3.985
|
| DEMetro_Z_vs_SMC |
2
|
21.317
|
2.9e-19
|
3.892
|
| DEMetro_Z_vs_SMC |
3
|
19.700
|
2.47e-18
|
3.597
|
| DEMetro_Z_vs_SMC |
4
|
24.773
|
4.62e-21
|
4.523
|
| DEMetro_Z_vs_SMC |
5
|
14.150
|
1.5e-14
|
2.584
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.148 |
0.070 |
0.022 |
3.525 |
| HMC |
2.5 |
0.068 |
0.047 |
0.008 |
2.606 |
| HMC |
3.0 |
0.059 |
0.038 |
0.006 |
3.771 |
| HMC |
4.0 |
0.036 |
0.032 |
0.004 |
0.809 |
| HMC |
10.0 |
0.023 |
0.024 |
0.003 |
-0.675 |
| HMC |
50.0 |
0.019 |
0.022 |
0.002 |
-1.478 |
| SMC |
2.1 |
0.201 |
0.070 |
0.022 |
5.916 |
| SMC |
2.5 |
0.189 |
0.047 |
0.008 |
17.450 |
| SMC |
3.0 |
0.178 |
0.038 |
0.006 |
25.278 |
| SMC |
4.0 |
0.176 |
0.032 |
0.004 |
34.797 |
| SMC |
10.0 |
0.106 |
0.024 |
0.003 |
32.675 |
| SMC |
50.0 |
0.035 |
0.022 |
0.002 |
5.764 |
| Metro |
2.1 |
0.364 |
0.070 |
0.022 |
13.232 |
| Metro |
2.5 |
0.138 |
0.047 |
0.008 |
11.191 |
| Metro |
3.0 |
0.083 |
0.038 |
0.006 |
8.217 |
| Metro |
4.0 |
0.070 |
0.032 |
0.004 |
9.045 |
| Metro |
10.0 |
0.050 |
0.024 |
0.003 |
10.199 |
| Metro |
50.0 |
0.042 |
0.022 |
0.002 |
8.846 |
| DEMetro_Z |
2.1 |
7.928 |
0.070 |
0.022 |
353.621 |
| DEMetro_Z |
2.5 |
4.096 |
0.047 |
0.008 |
497.613 |
| DEMetro_Z |
3.0 |
2.018 |
0.038 |
0.006 |
357.048 |
| DEMetro_Z |
4.0 |
1.255 |
0.032 |
0.004 |
295.679 |
| DEMetro_Z |
10.0 |
0.976 |
0.024 |
0.003 |
380.531 |
| DEMetro_Z |
50.0 |
0.802 |
0.022 |
0.002 |
342.419 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.520 |
0.605 |
0.153 |
| HMC |
2.5 |
0.305 |
0.762 |
0.067 |
| HMC |
3.0 |
1.666 |
0.105 |
1.198 |
| HMC |
4.0 |
3.746 |
0.000603 |
1.889 |
| HMC |
10.0 |
5.062 |
1.33e-05 |
2.999 |
| HMC |
50.0 |
7.139 |
3.25e-09 |
2.318 |
| SMC |
2.1 |
26.482 |
2.44e-25 |
5.135 |
| SMC |
2.5 |
125.339 |
1.71e-61 |
44.504 |
| SMC |
3.0 |
103.236 |
5.13e-39 |
301.492 |
| SMC |
4.0 |
83.257 |
4.46e-36 |
1640.752 |
| SMC |
10.0 |
102.240 |
1.19e-38 |
5057.956 |
| SMC |
50.0 |
62.318 |
1.15e-32 |
170.777 |
| Metro |
2.1 |
2.683 |
0.0115 |
2.221 |
| Metro |
2.5 |
1.243 |
0.224 |
1.995 |
| Metro |
3.0 |
2.371 |
0.0242 |
2.623 |
| Metro |
4.0 |
1.784 |
0.085 |
12.503 |
| Metro |
10.0 |
11.502 |
6.47e-13 |
9.362 |
| Metro |
50.0 |
13.489 |
8.49e-16 |
7.132 |
| DEMetro_Z |
2.1 |
15.707 |
8.88e-16 |
49.350 |
| DEMetro_Z |
2.5 |
15.818 |
8.24e-16 |
109.657 |
| DEMetro_Z |
3.0 |
17.467 |
6.14e-17 |
184.667 |
| DEMetro_Z |
4.0 |
14.912 |
3.91e-15 |
448.141 |
| DEMetro_Z |
10.0 |
15.407 |
1.68e-15 |
1850.328 |
| DEMetro_Z |
50.0 |
7.955 |
8.98e-09 |
1556.242 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-21.286
|
3.01e-19
|
-3.886
|
| HMC_vs_SMC |
1
|
-126.808
|
2.34e-41
|
-23.152
|
| HMC_vs_SMC |
2
|
-105.321
|
5.05e-39
|
-19.229
|
| HMC_vs_SMC |
3
|
-83.319
|
4.41e-36
|
-15.212
|
| HMC_vs_SMC |
4
|
-101.940
|
1.3e-38
|
-18.612
|
| HMC_vs_SMC |
5
|
-61.468
|
2.85e-32
|
-11.223
|
| Metro_vs_DEMetro_Z |
0
|
-15.320
|
1.94e-15
|
-2.797
|
| Metro_vs_DEMetro_Z |
1
|
-15.059
|
3.03e-15
|
-2.749
|
| Metro_vs_DEMetro_Z |
2
|
-17.145
|
1.02e-16
|
-3.130
|
| Metro_vs_DEMetro_Z |
3
|
-14.245
|
1.26e-14
|
-2.601
|
| Metro_vs_DEMetro_Z |
4
|
-15.318
|
1.95e-15
|
-2.797
|
| Metro_vs_DEMetro_Z |
5
|
-7.923
|
9.73e-09
|
-1.447
|
| HMC_vs_Metro |
0
|
-2.410
|
0.0225
|
-0.440
|
| HMC_vs_Metro |
1
|
-1.192
|
0.243
|
-0.218
|
| HMC_vs_Metro |
2
|
-1.095
|
0.282
|
-0.200
|
| HMC_vs_Metro |
3
|
-1.493
|
0.146
|
-0.273
|
| HMC_vs_Metro |
4
|
-6.608
|
3.05e-07
|
-1.206
|
| HMC_vs_Metro |
5
|
-9.742
|
1.19e-10
|
-1.779
|
| HMC_vs_DEMetro_Z |
0
|
-15.669
|
1.08e-15
|
-2.861
|
| HMC_vs_DEMetro_Z |
1
|
-15.782
|
8.99e-16
|
-2.881
|
| HMC_vs_DEMetro_Z |
2
|
-17.094
|
1.1e-16
|
-3.121
|
| HMC_vs_DEMetro_Z |
3
|
-14.870
|
4.21e-15
|
-2.715
|
| HMC_vs_DEMetro_Z |
4
|
-15.388
|
1.74e-15
|
-2.809
|
| HMC_vs_DEMetro_Z |
5
|
-7.945
|
9.2e-09
|
-1.451
|
| Metro_vs_SMC |
0
|
-3.633
|
0.00107
|
-0.663
|
| Metro_vs_SMC |
1
|
-26.651
|
6.06e-22
|
-4.866
|
| Metro_vs_SMC |
2
|
-92.976
|
1.86e-37
|
-16.975
|
| Metro_vs_SMC |
3
|
-83.315
|
4.42e-36
|
-15.211
|
| Metro_vs_SMC |
4
|
-102.253
|
1.19e-38
|
-18.669
|
| Metro_vs_SMC |
5
|
-59.863
|
6.1e-32
|
-10.929
|
| DEMetro_Z_vs_SMC |
0
|
14.011
|
1.92e-14
|
2.558
|
| DEMetro_Z_vs_SMC |
1
|
9.426
|
2.48e-10
|
1.721
|
| DEMetro_Z_vs_SMC |
2
|
-9.499
|
2.09e-10
|
-1.734
|
| DEMetro_Z_vs_SMC |
3
|
-30.358
|
1.57e-23
|
-5.543
|
| DEMetro_Z_vs_SMC |
4
|
-22.977
|
3.7e-20
|
-4.195
|
| DEMetro_Z_vs_SMC |
5
|
7.076
|
8.74e-08
|
1.292
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
12.205 |
9.489 |
17.780 |
0.153 |
| HMC |
2.5 |
2.137 |
1.990 |
2.209 |
0.067 |
| HMC |
3.0 |
0.961 |
0.588 |
0.312 |
1.198 |
| HMC |
4.0 |
0.257 |
0.165 |
0.049 |
1.889 |
| HMC |
10.0 |
0.067 |
0.049 |
0.006 |
2.999 |
| HMC |
50.0 |
0.045 |
0.035 |
0.004 |
2.318 |
| SMC |
2.1 |
100.791 |
9.489 |
17.780 |
5.135 |
| SMC |
2.5 |
100.315 |
1.990 |
2.209 |
44.504 |
| SMC |
3.0 |
94.553 |
0.588 |
0.312 |
301.492 |
| SMC |
4.0 |
80.555 |
0.165 |
0.049 |
1640.752 |
| SMC |
10.0 |
30.888 |
0.049 |
0.006 |
5057.956 |
| SMC |
50.0 |
0.778 |
0.035 |
0.004 |
170.777 |
| Metro |
2.1 |
48.985 |
9.489 |
17.780 |
2.221 |
| Metro |
2.5 |
6.398 |
1.990 |
2.209 |
1.995 |
| Metro |
3.0 |
1.406 |
0.588 |
0.312 |
2.623 |
| Metro |
4.0 |
0.777 |
0.165 |
0.049 |
12.503 |
| Metro |
10.0 |
0.106 |
0.049 |
0.006 |
9.362 |
| Metro |
50.0 |
0.066 |
0.035 |
0.004 |
7.132 |
| DEMetro_Z |
2.1 |
886.908 |
9.489 |
17.780 |
49.350 |
| DEMetro_Z |
2.5 |
244.260 |
1.990 |
2.209 |
109.657 |
| DEMetro_Z |
3.0 |
58.143 |
0.588 |
0.312 |
184.667 |
| DEMetro_Z |
4.0 |
22.122 |
0.165 |
0.049 |
448.141 |
| DEMetro_Z |
10.0 |
11.331 |
0.049 |
0.006 |
1850.328 |
| DEMetro_Z |
50.0 |
6.806 |
0.035 |
0.004 |
1556.242 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.182 |
1.48e-05 |
11.935 |
| HMC |
2.5 |
6.055 |
1.28e-06 |
12.327 |
| HMC |
3.0 |
4.879 |
3.53e-05 |
22.893 |
| HMC |
4.0 |
5.556 |
4.98e-06 |
8.880 |
| HMC |
10.0 |
3.834 |
0.000451 |
1.820 |
| HMC |
50.0 |
1.435 |
0.157 |
0.382 |
| SMC |
2.1 |
171.936 |
1.31e-46 |
229.807 |
| SMC |
2.5 |
239.923 |
8.76e-50 |
630.669 |
| SMC |
3.0 |
167.635 |
6.85e-45 |
1746.010 |
| SMC |
4.0 |
139.154 |
1.55e-42 |
2045.892 |
| SMC |
10.0 |
159.784 |
2.83e-44 |
2423.074 |
| SMC |
50.0 |
66.305 |
2.16e-33 |
208.797 |
| Metro |
2.1 |
5.183 |
1.52e-05 |
60.680 |
| Metro |
2.5 |
3.598 |
0.00118 |
34.900 |
| Metro |
3.0 |
6.900 |
1.37e-07 |
28.945 |
| Metro |
4.0 |
6.716 |
2.23e-07 |
25.122 |
| Metro |
10.0 |
23.295 |
3.01e-22 |
15.902 |
| Metro |
50.0 |
20.129 |
3.02e-20 |
13.811 |
| DEMetro_Z |
2.1 |
32.287 |
2.76e-24 |
716.506 |
| DEMetro_Z |
2.5 |
30.576 |
1.28e-23 |
995.835 |
| DEMetro_Z |
3.0 |
32.924 |
1.59e-24 |
1272.174 |
| DEMetro_Z |
4.0 |
27.927 |
1.63e-22 |
897.400 |
| DEMetro_Z |
10.0 |
28.417 |
1.01e-22 |
1221.009 |
| DEMetro_Z |
50.0 |
15.232 |
2.26e-15 |
979.939 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-27.962
|
1.58e-22
|
-5.105
|
| Metro_vs_DEMetro_Z |
1
|
-27.453
|
2.64e-22
|
-5.012
|
| Metro_vs_DEMetro_Z |
2
|
-32.378
|
2.56e-24
|
-5.911
|
| Metro_vs_DEMetro_Z |
3
|
-27.146
|
3.62e-22
|
-4.956
|
| Metro_vs_DEMetro_Z |
4
|
-28.021
|
1.49e-22
|
-5.116
|
| Metro_vs_DEMetro_Z |
5
|
-14.992
|
3.4e-15
|
-2.737
|
| DEMetro_Z_vs_SMC |
0
|
21.457
|
2.42e-19
|
3.917
|
| DEMetro_Z_vs_SMC |
1
|
11.248
|
4.29e-12
|
2.054
|
| DEMetro_Z_vs_SMC |
2
|
-10.640
|
1.58e-11
|
-1.943
|
| DEMetro_Z_vs_SMC |
3
|
-30.339
|
1.6e-23
|
-5.539
|
| DEMetro_Z_vs_SMC |
4
|
-24.952
|
3.79e-21
|
-4.556
|
| DEMetro_Z_vs_SMC |
5
|
11.966
|
9.7e-13
|
2.185
|
| HMC_vs_DEMetro_Z |
0
|
-32.734
|
1.88e-24
|
-5.976
|
| HMC_vs_DEMetro_Z |
1
|
-30.304
|
1.65e-23
|
-5.533
|
| HMC_vs_DEMetro_Z |
2
|
-32.113
|
3.23e-24
|
-5.863
|
| HMC_vs_DEMetro_Z |
3
|
-28.013
|
1.5e-22
|
-5.115
|
| HMC_vs_DEMetro_Z |
4
|
-28.357
|
1.07e-22
|
-5.177
|
| HMC_vs_DEMetro_Z |
5
|
-15.224
|
2.29e-15
|
-2.780
|
| HMC_vs_Metro |
0
|
-4.075
|
0.000326
|
-0.744
|
| HMC_vs_Metro |
1
|
-2.310
|
0.0282
|
-0.422
|
| HMC_vs_Metro |
2
|
-0.914
|
0.368
|
-0.167
|
| HMC_vs_Metro |
3
|
-4.107
|
0.000299
|
-0.750
|
| HMC_vs_Metro |
4
|
-16.713
|
2e-16
|
-3.051
|
| HMC_vs_Metro |
5
|
-19.925
|
1.82e-18
|
-3.638
|
| HMC_vs_SMC |
0
|
-80.253
|
1.3e-35
|
-14.652
|
| HMC_vs_SMC |
1
|
-185.069
|
4.11e-46
|
-33.789
|
| HMC_vs_SMC |
2
|
-158.938
|
3.38e-44
|
-29.018
|
| HMC_vs_SMC |
3
|
-137.307
|
2.34e-42
|
-25.069
|
| HMC_vs_SMC |
4
|
-158.285
|
3.81e-44
|
-28.899
|
| HMC_vs_SMC |
5
|
-66.558
|
2.88e-33
|
-12.152
|
| Metro_vs_SMC |
0
|
-14.758
|
5.1e-15
|
-2.694
|
| Metro_vs_SMC |
1
|
-58.068
|
1.46e-31
|
-10.602
|
| Metro_vs_SMC |
2
|
-142.905
|
7.36e-43
|
-26.091
|
| Metro_vs_SMC |
3
|
-140.742
|
1.14e-42
|
-25.696
|
| Metro_vs_SMC |
4
|
-158.917
|
3.39e-44
|
-29.014
|
| Metro_vs_SMC |
5
|
-59.626
|
6.83e-32
|
-10.886
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.466 |
0.118 |
0.029 |
11.935 |
| HMC |
2.5 |
0.215 |
0.084 |
0.011 |
12.327 |
| HMC |
3.0 |
0.150 |
0.064 |
0.004 |
22.893 |
| HMC |
4.0 |
0.075 |
0.049 |
0.003 |
8.880 |
| HMC |
10.0 |
0.037 |
0.034 |
0.001 |
1.820 |
| HMC |
50.0 |
0.030 |
0.029 |
0.001 |
0.382 |
| SMC |
2.1 |
6.822 |
0.118 |
0.029 |
229.807 |
| SMC |
2.5 |
6.785 |
0.084 |
0.011 |
630.669 |
| SMC |
3.0 |
6.608 |
0.064 |
0.004 |
1746.010 |
| SMC |
4.0 |
6.095 |
0.049 |
0.003 |
2045.892 |
| SMC |
10.0 |
3.630 |
0.034 |
0.001 |
2423.074 |
| SMC |
50.0 |
0.269 |
0.029 |
0.001 |
208.797 |
| Metro |
2.1 |
1.888 |
0.118 |
0.029 |
60.680 |
| Metro |
2.5 |
0.454 |
0.084 |
0.011 |
34.900 |
| Metro |
3.0 |
0.172 |
0.064 |
0.004 |
28.945 |
| Metro |
4.0 |
0.123 |
0.049 |
0.003 |
25.122 |
| Metro |
10.0 |
0.057 |
0.034 |
0.001 |
15.902 |
| Metro |
50.0 |
0.045 |
0.029 |
0.001 |
13.811 |
| DEMetro_Z |
2.1 |
21.021 |
0.118 |
0.029 |
716.506 |
| DEMetro_Z |
2.5 |
10.665 |
0.084 |
0.011 |
995.835 |
| DEMetro_Z |
3.0 |
4.832 |
0.064 |
0.004 |
1272.174 |
| DEMetro_Z |
4.0 |
2.701 |
0.049 |
0.003 |
897.400 |
| DEMetro_Z |
10.0 |
1.846 |
0.034 |
0.001 |
1221.009 |
| DEMetro_Z |
50.0 |
1.153 |
0.029 |
0.001 |
979.939 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.821 |
2.59e-06 |
48.828 |
| HMC |
2.5 |
5.793 |
2.79e-06 |
29.885 |
| HMC |
3.0 |
4.614 |
7.37e-05 |
22.439 |
| HMC |
4.0 |
4.947 |
2.73e-05 |
7.293 |
| HMC |
10.0 |
2.795 |
0.00729 |
0.907 |
| HMC |
50.0 |
-0.181 |
0.857 |
-0.044 |
| SMC |
2.1 |
162.836 |
1.52e-45 |
251.405 |
| SMC |
2.5 |
183.333 |
6.15e-47 |
303.323 |
| SMC |
3.0 |
194.430 |
9.03e-48 |
309.901 |
| SMC |
4.0 |
172.441 |
4.77e-46 |
301.847 |
| SMC |
10.0 |
187.598 |
2.03e-47 |
284.323 |
| SMC |
50.0 |
64.637 |
6.68e-34 |
84.507 |
| Metro |
2.1 |
8.797 |
1.11e-09 |
124.659 |
| Metro |
2.5 |
6.895 |
1.41e-07 |
60.787 |
| Metro |
3.0 |
8.132 |
5.45e-09 |
25.122 |
| Metro |
4.0 |
14.051 |
1.09e-14 |
21.632 |
| Metro |
10.0 |
20.569 |
1.07e-21 |
10.962 |
| Metro |
50.0 |
18.762 |
1.17e-20 |
9.481 |
| DEMetro_Z |
2.1 |
87.765 |
6.99e-37 |
318.117 |
| DEMetro_Z |
2.5 |
88.113 |
6.72e-37 |
361.395 |
| DEMetro_Z |
3.0 |
91.626 |
2.02e-37 |
337.461 |
| DEMetro_Z |
4.0 |
80.861 |
7.74e-36 |
305.384 |
| DEMetro_Z |
10.0 |
73.338 |
1.38e-34 |
301.955 |
| DEMetro_Z |
50.0 |
39.670 |
7.63e-27 |
299.619 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
16.743
|
1.91e-16
|
3.057
|
| DEMetro_Z_vs_SMC |
1
|
11.752
|
1.5e-12
|
2.146
|
| DEMetro_Z_vs_SMC |
2
|
7.100
|
8.21e-08
|
1.296
|
| DEMetro_Z_vs_SMC |
3
|
0.857
|
0.398
|
0.156
|
| DEMetro_Z_vs_SMC |
4
|
3.607
|
0.00115
|
0.658
|
| DEMetro_Z_vs_SMC |
5
|
28.345
|
1.08e-22
|
5.175
|
| HMC_vs_Metro |
0
|
-4.411
|
0.00013
|
-0.805
|
| HMC_vs_Metro |
1
|
-3.004
|
0.00545
|
-0.548
|
| HMC_vs_Metro |
2
|
-0.439
|
0.664
|
-0.080
|
| HMC_vs_Metro |
3
|
-7.463
|
3.18e-08
|
-1.363
|
| HMC_vs_Metro |
4
|
-16.641
|
2.24e-16
|
-3.038
|
| HMC_vs_Metro |
5
|
-19.256
|
4.58e-18
|
-3.516
|
| Metro_vs_DEMetro_Z |
0
|
-13.544
|
4.53e-14
|
-2.473
|
| Metro_vs_DEMetro_Z |
1
|
-35.501
|
1.89e-25
|
-6.482
|
| Metro_vs_DEMetro_Z |
2
|
-63.484
|
1.12e-32
|
-11.591
|
| Metro_vs_DEMetro_Z |
3
|
-76.385
|
5.42e-35
|
-13.946
|
| Metro_vs_DEMetro_Z |
4
|
-70.594
|
5.27e-34
|
-12.889
|
| Metro_vs_DEMetro_Z |
5
|
-37.982
|
2.77e-26
|
-6.934
|
| HMC_vs_SMC |
0
|
-23.972
|
1.15e-20
|
-4.377
|
| HMC_vs_SMC |
1
|
-48.089
|
3.28e-29
|
-8.780
|
| HMC_vs_SMC |
2
|
-60.796
|
3.91e-32
|
-11.100
|
| HMC_vs_SMC |
3
|
-151.736
|
1.3e-43
|
-27.703
|
| HMC_vs_SMC |
4
|
-178.797
|
1.12e-45
|
-32.644
|
| HMC_vs_SMC |
5
|
-64.102
|
8.51e-33
|
-11.703
|
| Metro_vs_SMC |
0
|
-8.827
|
1.03e-09
|
-1.612
|
| Metro_vs_SMC |
1
|
-25.888
|
1.36e-21
|
-4.727
|
| Metro_vs_SMC |
2
|
-75.300
|
8.2e-35
|
-13.748
|
| Metro_vs_SMC |
3
|
-136.341
|
2.87e-42
|
-24.892
|
| Metro_vs_SMC |
4
|
-170.020
|
4.8e-45
|
-31.041
|
| Metro_vs_SMC |
5
|
-53.822
|
1.3e-30
|
-9.826
|
| HMC_vs_DEMetro_Z |
0
|
-26.946
|
4.45e-22
|
-4.920
|
| HMC_vs_DEMetro_Z |
1
|
-53.509
|
1.53e-30
|
-9.769
|
| HMC_vs_DEMetro_Z |
2
|
-51.620
|
4.31e-30
|
-9.424
|
| HMC_vs_DEMetro_Z |
3
|
-79.345
|
1.81e-35
|
-14.486
|
| HMC_vs_DEMetro_Z |
4
|
-73.695
|
1.53e-34
|
-13.455
|
| HMC_vs_DEMetro_Z |
5
|
-39.678
|
7.99e-27
|
-7.244
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.088 |
0.015 |
0.001 |
48.828 |
| HMC |
2.5 |
0.053 |
0.015 |
0.001 |
29.885 |
| HMC |
3.0 |
0.043 |
0.015 |
0.001 |
22.439 |
| HMC |
4.0 |
0.025 |
0.015 |
0.001 |
7.293 |
| HMC |
10.0 |
0.015 |
0.014 |
0.001 |
0.907 |
| HMC |
50.0 |
0.014 |
0.014 |
0.001 |
-0.044 |
| SMC |
2.1 |
0.392 |
0.015 |
0.001 |
251.405 |
| SMC |
2.5 |
0.399 |
0.015 |
0.001 |
303.323 |
| SMC |
3.0 |
0.408 |
0.015 |
0.001 |
309.901 |
| SMC |
4.0 |
0.410 |
0.015 |
0.001 |
301.847 |
| SMC |
10.0 |
0.381 |
0.014 |
0.001 |
284.323 |
| SMC |
50.0 |
0.111 |
0.014 |
0.001 |
84.507 |
| Metro |
2.1 |
0.202 |
0.015 |
0.001 |
124.659 |
| Metro |
2.5 |
0.092 |
0.015 |
0.001 |
60.787 |
| Metro |
3.0 |
0.047 |
0.015 |
0.001 |
25.122 |
| Metro |
4.0 |
0.043 |
0.015 |
0.001 |
21.632 |
| Metro |
10.0 |
0.028 |
0.014 |
0.001 |
10.962 |
| Metro |
50.0 |
0.025 |
0.014 |
0.001 |
9.481 |
| DEMetro_Z |
2.1 |
0.492 |
0.015 |
0.001 |
318.117 |
| DEMetro_Z |
2.5 |
0.473 |
0.015 |
0.001 |
361.395 |
| DEMetro_Z |
3.0 |
0.443 |
0.015 |
0.001 |
337.461 |
| DEMetro_Z |
4.0 |
0.414 |
0.015 |
0.001 |
305.384 |
| DEMetro_Z |
10.0 |
0.404 |
0.014 |
0.001 |
301.955 |
| DEMetro_Z |
50.0 |
0.357 |
0.014 |
0.001 |
299.619 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.620 |
0.116 |
7.235 |
| HMC |
2.5 |
1.454 |
0.157 |
5.020 |
| HMC |
3.0 |
1.720 |
0.096 |
4.921 |
| HMC |
4.0 |
-2.718 |
0.00878 |
-0.809 |
| HMC |
10.0 |
-1.542 |
0.129 |
-0.438 |
| HMC |
50.0 |
-5.897 |
2.03e-07 |
-1.476 |
| SMC |
2.1 |
16.497 |
3.63e-19 |
7.772 |
| SMC |
2.5 |
28.776 |
7.96e-25 |
21.273 |
| SMC |
3.0 |
24.374 |
1.62e-21 |
28.850 |
| SMC |
4.0 |
33.591 |
8.04e-26 |
35.498 |
| SMC |
10.0 |
21.312 |
1.34e-19 |
32.995 |
| SMC |
50.0 |
10.003 |
2.47e-12 |
4.680 |
| Metro |
2.1 |
5.634 |
3.95e-06 |
8.457 |
| Metro |
2.5 |
10.454 |
6.37e-12 |
8.021 |
| Metro |
3.0 |
8.894 |
4.5e-10 |
8.341 |
| Metro |
4.0 |
17.468 |
1.75e-21 |
6.774 |
| Metro |
10.0 |
18.664 |
6.9e-20 |
10.785 |
| Metro |
50.0 |
17.028 |
2.49e-19 |
8.463 |
| DEMetro_Z |
2.1 |
21.818 |
1.52e-19 |
335.434 |
| DEMetro_Z |
2.5 |
19.730 |
2.37e-18 |
471.028 |
| DEMetro_Z |
3.0 |
16.636 |
2.25e-16 |
364.157 |
| DEMetro_Z |
4.0 |
23.857 |
1.29e-20 |
270.061 |
| DEMetro_Z |
10.0 |
21.419 |
2.53e-19 |
383.275 |
| DEMetro_Z |
50.0 |
15.970 |
6.58e-16 |
296.183 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-20.526
|
8.12e-19
|
-3.747
|
| HMC_vs_DEMetro_Z |
1
|
-19.770
|
2.25e-18
|
-3.610
|
| HMC_vs_DEMetro_Z |
2
|
-15.968
|
6.62e-16
|
-2.915
|
| HMC_vs_DEMetro_Z |
3
|
-23.914
|
1.23e-20
|
-4.366
|
| HMC_vs_DEMetro_Z |
4
|
-21.377
|
2.68e-19
|
-3.903
|
| HMC_vs_DEMetro_Z |
5
|
-16.060
|
5.7e-16
|
-2.932
|
| Metro_vs_SMC |
0
|
0.395
|
0.695
|
0.072
|
| Metro_vs_SMC |
1
|
-12.404
|
4.03e-13
|
-2.265
|
| Metro_vs_SMC |
2
|
-13.021
|
1.22e-13
|
-2.377
|
| Metro_vs_SMC |
3
|
-25.349
|
2.44e-21
|
-4.628
|
| Metro_vs_SMC |
4
|
-13.825
|
2.7e-14
|
-2.524
|
| Metro_vs_SMC |
5
|
5.509
|
6.18e-06
|
1.006
|
| Metro_vs_DEMetro_Z |
0
|
-21.376
|
2.69e-19
|
-3.903
|
| Metro_vs_DEMetro_Z |
1
|
-19.118
|
5.55e-18
|
-3.490
|
| Metro_vs_DEMetro_Z |
2
|
-16.183
|
4.67e-16
|
-2.955
|
| Metro_vs_DEMetro_Z |
3
|
-23.416
|
2.2e-20
|
-4.275
|
| Metro_vs_DEMetro_Z |
4
|
-20.840
|
5.37e-19
|
-3.805
|
| Metro_vs_DEMetro_Z |
5
|
-15.473
|
1.5e-15
|
-2.825
|
| HMC_vs_Metro |
0
|
-0.269
|
0.79
|
-0.049
|
| HMC_vs_Metro |
1
|
-0.833
|
0.412
|
-0.152
|
| HMC_vs_Metro |
2
|
-1.208
|
0.237
|
-0.221
|
| HMC_vs_Metro |
3
|
-17.432
|
6.57e-17
|
-3.183
|
| HMC_vs_Metro |
4
|
-18.420
|
1.51e-17
|
-3.363
|
| HMC_vs_Metro |
5
|
-20.923
|
4.81e-19
|
-3.820
|
| HMC_vs_SMC |
0
|
-0.118
|
0.907
|
-0.022
|
| HMC_vs_SMC |
1
|
-4.648
|
6.75e-05
|
-0.849
|
| HMC_vs_SMC |
2
|
-9.614
|
1.6e-10
|
-1.755
|
| HMC_vs_SMC |
3
|
-31.990
|
3.6e-24
|
-5.841
|
| HMC_vs_SMC |
4
|
-22.095
|
1.09e-19
|
-4.034
|
| HMC_vs_SMC |
5
|
-14.873
|
4.18e-15
|
-2.715
|
| DEMetro_Z_vs_SMC |
0
|
21.104
|
3.81e-19
|
3.853
|
| DEMetro_Z_vs_SMC |
1
|
18.904
|
7.52e-18
|
3.451
|
| DEMetro_Z_vs_SMC |
2
|
15.314
|
1.97e-15
|
2.796
|
| DEMetro_Z_vs_SMC |
3
|
20.264
|
1.15e-18
|
3.700
|
| DEMetro_Z_vs_SMC |
4
|
19.344
|
4.05e-18
|
3.532
|
| DEMetro_Z_vs_SMC |
5
|
15.785
|
8.94e-16
|
2.882
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.231 |
0.070 |
0.022 |
7.235 |
| HMC |
2.5 |
0.088 |
0.047 |
0.008 |
5.020 |
| HMC |
3.0 |
0.065 |
0.038 |
0.006 |
4.921 |
| HMC |
4.0 |
0.029 |
0.032 |
0.004 |
-0.809 |
| HMC |
10.0 |
0.023 |
0.024 |
0.003 |
-0.438 |
| HMC |
50.0 |
0.019 |
0.022 |
0.002 |
-1.476 |
| SMC |
2.1 |
0.243 |
0.070 |
0.022 |
7.772 |
| SMC |
2.5 |
0.220 |
0.047 |
0.008 |
21.273 |
| SMC |
3.0 |
0.198 |
0.038 |
0.006 |
28.850 |
| SMC |
4.0 |
0.179 |
0.032 |
0.004 |
35.498 |
| SMC |
10.0 |
0.107 |
0.024 |
0.003 |
32.995 |
| SMC |
50.0 |
0.033 |
0.022 |
0.002 |
4.680 |
| Metro |
2.1 |
0.258 |
0.070 |
0.022 |
8.457 |
| Metro |
2.5 |
0.112 |
0.047 |
0.008 |
8.021 |
| Metro |
3.0 |
0.084 |
0.038 |
0.006 |
8.341 |
| Metro |
4.0 |
0.060 |
0.032 |
0.004 |
6.774 |
| Metro |
10.0 |
0.051 |
0.024 |
0.003 |
10.785 |
| Metro |
50.0 |
0.042 |
0.022 |
0.002 |
8.463 |
| DEMetro_Z |
2.1 |
7.524 |
0.070 |
0.022 |
335.434 |
| DEMetro_Z |
2.5 |
3.880 |
0.047 |
0.008 |
471.028 |
| DEMetro_Z |
3.0 |
2.057 |
0.038 |
0.006 |
364.157 |
| DEMetro_Z |
4.0 |
1.149 |
0.032 |
0.004 |
270.061 |
| DEMetro_Z |
10.0 |
0.983 |
0.024 |
0.003 |
383.275 |
| DEMetro_Z |
50.0 |
0.696 |
0.022 |
0.002 |
296.183 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.098 |
0.923 |
0.023 |
| HMC |
2.5 |
1.062 |
0.295 |
0.550 |
| HMC |
3.0 |
2.572 |
0.0144 |
1.452 |
| HMC |
4.0 |
3.626 |
0.000985 |
2.933 |
| HMC |
10.0 |
5.636 |
1.84e-06 |
2.816 |
| HMC |
50.0 |
8.063 |
7.33e-11 |
2.410 |
| SMC |
2.1 |
22.936 |
1.27e-29 |
5.277 |
| SMC |
2.5 |
52.280 |
2.27e-32 |
44.842 |
| SMC |
3.0 |
50.932 |
5.7e-30 |
291.564 |
| SMC |
4.0 |
48.227 |
3.02e-29 |
1544.738 |
| SMC |
10.0 |
30.197 |
1.83e-23 |
4121.787 |
| SMC |
50.0 |
25.670 |
1.6e-21 |
142.352 |
| Metro |
2.1 |
1.367 |
0.182 |
1.377 |
| Metro |
2.5 |
0.458 |
0.649 |
0.101 |
| Metro |
3.0 |
2.664 |
0.0118 |
1.818 |
| Metro |
4.0 |
5.358 |
7.32e-06 |
4.783 |
| Metro |
10.0 |
11.679 |
4.87e-13 |
9.917 |
| Metro |
50.0 |
17.436 |
9.94e-21 |
7.386 |
| DEMetro_Z |
2.1 |
7.256 |
5.28e-08 |
25.758 |
| DEMetro_Z |
2.5 |
9.786 |
1.05e-10 |
50.343 |
| DEMetro_Z |
3.0 |
8.549 |
2.03e-09 |
86.660 |
| DEMetro_Z |
4.0 |
11.929 |
1.04e-12 |
152.168 |
| DEMetro_Z |
10.0 |
6.776 |
1.94e-07 |
700.842 |
| DEMetro_Z |
50.0 |
5.613 |
4.62e-06 |
553.183 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-23.804
|
1.39e-20
|
-4.346
|
| HMC_vs_SMC |
1
|
-49.439
|
1.49e-29
|
-9.026
|
| HMC_vs_SMC |
2
|
-50.870
|
6.55e-30
|
-9.287
|
| HMC_vs_SMC |
3
|
-48.272
|
2.95e-29
|
-8.813
|
| HMC_vs_SMC |
4
|
-30.192
|
1.84e-23
|
-5.512
|
| HMC_vs_SMC |
5
|
-25.334
|
2.48e-21
|
-4.625
|
| Metro_vs_DEMetro_Z |
0
|
-7.803
|
1.32e-08
|
-1.425
|
| Metro_vs_DEMetro_Z |
1
|
-9.728
|
1.23e-10
|
-1.776
|
| Metro_vs_DEMetro_Z |
2
|
-8.513
|
2.22e-09
|
-1.554
|
| Metro_vs_DEMetro_Z |
3
|
-11.610
|
2.01e-12
|
-2.120
|
| Metro_vs_DEMetro_Z |
4
|
-6.691
|
2.44e-07
|
-1.222
|
| Metro_vs_DEMetro_Z |
5
|
-5.540
|
5.66e-06
|
-1.012
|
| HMC_vs_Metro |
0
|
-1.336
|
0.192
|
-0.244
|
| HMC_vs_Metro |
1
|
0.915
|
0.368
|
0.167
|
| HMC_vs_Metro |
2
|
-0.462
|
0.647
|
-0.084
|
| HMC_vs_Metro |
3
|
-1.512
|
0.141
|
-0.276
|
| HMC_vs_Metro |
4
|
-7.648
|
1.97e-08
|
-1.396
|
| HMC_vs_Metro |
5
|
-12.851
|
1.69e-13
|
-2.346
|
| HMC_vs_DEMetro_Z |
0
|
-7.219
|
6e-08
|
-1.318
|
| HMC_vs_DEMetro_Z |
1
|
-9.451
|
2.34e-10
|
-1.726
|
| HMC_vs_DEMetro_Z |
2
|
-8.498
|
2.31e-09
|
-1.551
|
| HMC_vs_DEMetro_Z |
3
|
-11.627
|
1.94e-12
|
-2.123
|
| HMC_vs_DEMetro_Z |
4
|
-6.754
|
2.06e-07
|
-1.233
|
| HMC_vs_DEMetro_Z |
5
|
-5.585
|
5e-06
|
-1.020
|
| Metro_vs_SMC |
0
|
-3.818
|
0.000654
|
-0.697
|
| Metro_vs_SMC |
1
|
-53.331
|
1.69e-30
|
-9.737
|
| Metro_vs_SMC |
2
|
-50.416
|
8.48e-30
|
-9.205
|
| Metro_vs_SMC |
3
|
-47.883
|
3.72e-29
|
-8.742
|
| Metro_vs_SMC |
4
|
-30.089
|
2.02e-23
|
-5.494
|
| Metro_vs_SMC |
5
|
-24.593
|
5.66e-21
|
-4.490
|
| DEMetro_Z_vs_SMC |
0
|
5.723
|
3.41e-06
|
1.045
|
| DEMetro_Z_vs_SMC |
1
|
1.016
|
0.318
|
0.186
|
| DEMetro_Z_vs_SMC |
2
|
-17.435
|
6.54e-17
|
-3.183
|
| DEMetro_Z_vs_SMC |
3
|
-37.446
|
4.15e-26
|
-6.837
|
| DEMetro_Z_vs_SMC |
4
|
-19.748
|
2.31e-18
|
-3.606
|
| DEMetro_Z_vs_SMC |
5
|
4.169
|
0.000253
|
0.761
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
9.904 |
9.489 |
17.780 |
0.023 |
| HMC |
2.5 |
3.204 |
1.990 |
2.209 |
0.550 |
| HMC |
3.0 |
1.040 |
0.588 |
0.312 |
1.452 |
| HMC |
4.0 |
0.309 |
0.165 |
0.049 |
2.933 |
| HMC |
10.0 |
0.066 |
0.049 |
0.006 |
2.816 |
| HMC |
50.0 |
0.045 |
0.035 |
0.004 |
2.410 |
| SMC |
2.1 |
103.311 |
9.489 |
17.780 |
5.277 |
| SMC |
2.5 |
101.062 |
1.990 |
2.209 |
44.842 |
| SMC |
3.0 |
91.459 |
0.588 |
0.312 |
291.564 |
| SMC |
4.0 |
75.851 |
0.165 |
0.049 |
1544.738 |
| SMC |
10.0 |
25.180 |
0.049 |
0.006 |
4121.787 |
| SMC |
50.0 |
0.654 |
0.035 |
0.004 |
142.352 |
| Metro |
2.1 |
33.967 |
9.489 |
17.780 |
1.377 |
| Metro |
2.5 |
2.212 |
1.990 |
2.209 |
0.101 |
| Metro |
3.0 |
1.155 |
0.588 |
0.312 |
1.818 |
| Metro |
4.0 |
0.399 |
0.165 |
0.049 |
4.783 |
| Metro |
10.0 |
0.109 |
0.049 |
0.006 |
9.917 |
| Metro |
50.0 |
0.067 |
0.035 |
0.004 |
7.386 |
| DEMetro_Z |
2.1 |
467.455 |
9.489 |
17.780 |
25.758 |
| DEMetro_Z |
2.5 |
113.215 |
1.990 |
2.209 |
50.343 |
| DEMetro_Z |
3.0 |
27.597 |
0.588 |
0.312 |
86.660 |
| DEMetro_Z |
4.0 |
7.620 |
0.165 |
0.049 |
152.168 |
| DEMetro_Z |
10.0 |
4.322 |
0.049 |
0.006 |
700.842 |
| DEMetro_Z |
50.0 |
2.441 |
0.035 |
0.004 |
553.183 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.567 |
0.00127 |
12.679 |
| HMC |
2.5 |
3.439 |
0.00178 |
15.519 |
| HMC |
3.0 |
3.877 |
0.000557 |
28.514 |
| HMC |
4.0 |
2.721 |
0.0108 |
5.916 |
| HMC |
10.0 |
3.897 |
0.000347 |
1.647 |
| HMC |
50.0 |
0.609 |
0.545 |
0.158 |
| SMC |
2.1 |
72.996 |
1.32e-34 |
229.327 |
| SMC |
2.5 |
89.213 |
5.59e-37 |
622.993 |
| SMC |
3.0 |
87.797 |
9.61e-37 |
1686.790 |
| SMC |
4.0 |
81.869 |
7.27e-36 |
1954.750 |
| SMC |
10.0 |
46.649 |
7.83e-29 |
2132.137 |
| SMC |
50.0 |
26.264 |
8.67e-22 |
176.587 |
| Metro |
2.1 |
3.083 |
0.00446 |
31.239 |
| Metro |
2.5 |
7.898 |
9.67e-09 |
20.521 |
| Metro |
3.0 |
5.620 |
4.51e-06 |
32.578 |
| Metro |
4.0 |
8.820 |
9.11e-10 |
17.843 |
| Metro |
10.0 |
19.224 |
4.74e-19 |
16.490 |
| Metro |
50.0 |
22.227 |
3.26e-22 |
13.222 |
| DEMetro_Z |
2.1 |
19.059 |
6.02e-18 |
520.306 |
| DEMetro_Z |
2.5 |
18.069 |
2.52e-17 |
663.069 |
| DEMetro_Z |
3.0 |
15.364 |
1.8e-15 |
831.852 |
| DEMetro_Z |
4.0 |
24.947 |
3.79e-21 |
517.075 |
| DEMetro_Z |
10.0 |
18.815 |
8.53e-18 |
749.813 |
| DEMetro_Z |
50.0 |
15.207 |
2.35e-15 |
581.079 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-20.868
|
5.17e-19
|
-3.810
|
| Metro_vs_DEMetro_Z |
1
|
-17.080
|
1.13e-16
|
-3.118
|
| Metro_vs_DEMetro_Z |
2
|
-15.187
|
2.44e-15
|
-2.773
|
| Metro_vs_DEMetro_Z |
3
|
-24.374
|
7.25e-21
|
-4.450
|
| Metro_vs_DEMetro_Z |
4
|
-18.469
|
1.4e-17
|
-3.372
|
| Metro_vs_DEMetro_Z |
5
|
-14.853
|
4.33e-15
|
-2.712
|
| DEMetro_Z_vs_SMC |
0
|
10.321
|
3.21e-11
|
1.884
|
| DEMetro_Z_vs_SMC |
1
|
1.038
|
0.308
|
0.189
|
| DEMetro_Z_vs_SMC |
2
|
-14.392
|
9.72e-15
|
-2.628
|
| DEMetro_Z_vs_SMC |
3
|
-41.750
|
1.87e-27
|
-7.623
|
| DEMetro_Z_vs_SMC |
4
|
-22.555
|
6.16e-20
|
-4.118
|
| DEMetro_Z_vs_SMC |
5
|
10.556
|
1.91e-11
|
1.927
|
| HMC_vs_DEMetro_Z |
0
|
-18.708
|
9.95e-18
|
-3.416
|
| HMC_vs_DEMetro_Z |
1
|
-18.046
|
2.61e-17
|
-3.295
|
| HMC_vs_DEMetro_Z |
2
|
-14.642
|
6.26e-15
|
-2.673
|
| HMC_vs_DEMetro_Z |
3
|
-24.128
|
9.61e-21
|
-4.405
|
| HMC_vs_DEMetro_Z |
4
|
-18.785
|
8.91e-18
|
-3.430
|
| HMC_vs_DEMetro_Z |
5
|
-15.206
|
2.36e-15
|
-2.776
|
| HMC_vs_Metro |
0
|
-1.682
|
0.103
|
-0.307
|
| HMC_vs_Metro |
1
|
-0.882
|
0.385
|
-0.161
|
| HMC_vs_Metro |
2
|
-0.561
|
0.579
|
-0.102
|
| HMC_vs_Metro |
3
|
-3.706
|
0.000883
|
-0.677
|
| HMC_vs_Metro |
4
|
-15.313
|
1.97e-15
|
-2.796
|
| HMC_vs_Metro |
5
|
-22.418
|
7.28e-20
|
-4.093
|
| HMC_vs_SMC |
0
|
-40.692
|
3.89e-27
|
-7.429
|
| HMC_vs_SMC |
1
|
-74.288
|
1.21e-34
|
-13.563
|
| HMC_vs_SMC |
2
|
-87.115
|
1.22e-36
|
-15.905
|
| HMC_vs_SMC |
3
|
-81.327
|
8.88e-36
|
-14.848
|
| HMC_vs_SMC |
4
|
-46.680
|
7.7e-29
|
-8.523
|
| HMC_vs_SMC |
5
|
-26.404
|
7.85e-22
|
-4.821
|
| Metro_vs_SMC |
0
|
-17.483
|
6.07e-17
|
-3.192
|
| Metro_vs_SMC |
1
|
-82.049
|
6.88e-36
|
-14.980
|
| Metro_vs_SMC |
2
|
-83.561
|
4.06e-36
|
-15.256
|
| Metro_vs_SMC |
3
|
-79.624
|
1.64e-35
|
-14.537
|
| Metro_vs_SMC |
4
|
-46.083
|
1.11e-28
|
-8.414
|
| Metro_vs_SMC |
5
|
-24.076
|
1.02e-20
|
-4.396
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.488 |
0.118 |
0.029 |
12.679 |
| HMC |
2.5 |
0.249 |
0.084 |
0.011 |
15.519 |
| HMC |
3.0 |
0.171 |
0.064 |
0.004 |
28.514 |
| HMC |
4.0 |
0.067 |
0.049 |
0.003 |
5.916 |
| HMC |
10.0 |
0.036 |
0.034 |
0.001 |
1.647 |
| HMC |
50.0 |
0.030 |
0.029 |
0.001 |
0.158 |
| SMC |
2.1 |
6.808 |
0.118 |
0.029 |
229.327 |
| SMC |
2.5 |
6.703 |
0.084 |
0.011 |
622.993 |
| SMC |
3.0 |
6.386 |
0.064 |
0.004 |
1686.790 |
| SMC |
4.0 |
5.825 |
0.049 |
0.003 |
1954.750 |
| SMC |
10.0 |
3.199 |
0.034 |
0.001 |
2132.137 |
| SMC |
50.0 |
0.232 |
0.029 |
0.001 |
176.587 |
| Metro |
2.1 |
1.029 |
0.118 |
0.029 |
31.239 |
| Metro |
2.5 |
0.302 |
0.084 |
0.011 |
20.521 |
| Metro |
3.0 |
0.186 |
0.064 |
0.004 |
32.578 |
| Metro |
4.0 |
0.102 |
0.049 |
0.003 |
17.843 |
| Metro |
10.0 |
0.058 |
0.034 |
0.001 |
16.490 |
| Metro |
50.0 |
0.044 |
0.029 |
0.001 |
13.222 |
| DEMetro_Z |
2.1 |
15.297 |
0.118 |
0.029 |
520.306 |
| DEMetro_Z |
2.5 |
7.129 |
0.084 |
0.011 |
663.069 |
| DEMetro_Z |
3.0 |
3.182 |
0.064 |
0.004 |
831.852 |
| DEMetro_Z |
4.0 |
1.577 |
0.049 |
0.003 |
517.075 |
| DEMetro_Z |
10.0 |
1.147 |
0.034 |
0.001 |
749.813 |
| DEMetro_Z |
50.0 |
0.696 |
0.029 |
0.001 |
581.079 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.752 |
0.0101 |
65.153 |
| HMC |
2.5 |
2.640 |
0.0132 |
34.880 |
| HMC |
3.0 |
3.323 |
0.00242 |
28.382 |
| HMC |
4.0 |
2.629 |
0.0134 |
4.505 |
| HMC |
10.0 |
2.982 |
0.00439 |
0.975 |
| HMC |
50.0 |
-1.232 |
0.223 |
-0.296 |
| SMC |
2.1 |
136.359 |
6.54e-43 |
259.847 |
| SMC |
2.5 |
152.519 |
2.98e-44 |
313.107 |
| SMC |
3.0 |
155.527 |
1.67e-44 |
318.585 |
| SMC |
4.0 |
166.160 |
1.69e-45 |
304.653 |
| SMC |
10.0 |
168.770 |
7.33e-46 |
280.634 |
| SMC |
50.0 |
29.071 |
3.63e-23 |
72.818 |
| Metro |
2.1 |
7.794 |
1.35e-08 |
87.212 |
| Metro |
2.5 |
9.658 |
1.41e-10 |
52.644 |
| Metro |
3.0 |
7.178 |
6.55e-08 |
31.868 |
| Metro |
4.0 |
10.562 |
1.41e-11 |
17.313 |
| Metro |
10.0 |
20.031 |
8.26e-21 |
11.751 |
| Metro |
50.0 |
18.503 |
1.7e-20 |
9.281 |
| DEMetro_Z |
2.1 |
43.625 |
5.09e-28 |
352.755 |
| DEMetro_Z |
2.5 |
68.589 |
1.07e-33 |
392.751 |
| DEMetro_Z |
3.0 |
44.935 |
2.18e-28 |
352.584 |
| DEMetro_Z |
4.0 |
38.533 |
1.75e-26 |
294.440 |
| DEMetro_Z |
10.0 |
41.523 |
2.06e-27 |
294.646 |
| DEMetro_Z |
50.0 |
27.438 |
2.62e-22 |
250.495 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
10.748
|
1.25e-11
|
1.962
|
| DEMetro_Z_vs_SMC |
1
|
13.799
|
2.83e-14
|
2.519
|
| DEMetro_Z_vs_SMC |
2
|
4.227
|
0.000215
|
0.772
|
| DEMetro_Z_vs_SMC |
3
|
-1.313
|
0.199
|
-0.240
|
| DEMetro_Z_vs_SMC |
4
|
1.892
|
0.0685
|
0.345
|
| DEMetro_Z_vs_SMC |
5
|
18.842
|
8.21e-18
|
3.440
|
| HMC_vs_Metro |
0
|
-0.832
|
0.412
|
-0.152
|
| HMC_vs_Metro |
1
|
-1.147
|
0.261
|
-0.209
|
| HMC_vs_Metro |
2
|
-0.437
|
0.666
|
-0.080
|
| HMC_vs_Metro |
3
|
-4.943
|
2.97e-05
|
-0.903
|
| HMC_vs_Metro |
4
|
-17.683
|
4.49e-17
|
-3.228
|
| HMC_vs_Metro |
5
|
-18.572
|
1.21e-17
|
-3.391
|
| Metro_vs_DEMetro_Z |
0
|
-18.290
|
1.82e-17
|
-3.339
|
| Metro_vs_DEMetro_Z |
1
|
-43.809
|
4.73e-28
|
-7.998
|
| Metro_vs_DEMetro_Z |
2
|
-41.345
|
2.47e-27
|
-7.549
|
| Metro_vs_DEMetro_Z |
3
|
-36.411
|
9.21e-26
|
-6.648
|
| Metro_vs_DEMetro_Z |
4
|
-40.509
|
4.43e-27
|
-7.396
|
| Metro_vs_DEMetro_Z |
5
|
-26.438
|
7.57e-22
|
-4.827
|
| HMC_vs_SMC |
0
|
-8.389
|
3.03e-09
|
-1.532
|
| HMC_vs_SMC |
1
|
-21.538
|
2.18e-19
|
-3.932
|
| HMC_vs_SMC |
2
|
-33.231
|
1.23e-24
|
-6.067
|
| HMC_vs_SMC |
3
|
-118.631
|
1.61e-40
|
-21.659
|
| HMC_vs_SMC |
4
|
-166.927
|
8.17e-45
|
-30.477
|
| HMC_vs_SMC |
5
|
-29.480
|
3.59e-23
|
-5.382
|
| Metro_vs_SMC |
0
|
-15.109
|
2.79e-15
|
-2.759
|
| Metro_vs_SMC |
1
|
-48.578
|
2.46e-29
|
-8.869
|
| Metro_vs_SMC |
2
|
-57.028
|
2.46e-31
|
-10.412
|
| Metro_vs_SMC |
3
|
-108.530
|
2.12e-39
|
-19.815
|
| Metro_vs_SMC |
4
|
-152.847
|
1.05e-43
|
-27.906
|
| Metro_vs_SMC |
5
|
-24.665
|
5.22e-21
|
-4.503
|
| HMC_vs_DEMetro_Z |
0
|
-10.673
|
1.48e-11
|
-1.949
|
| HMC_vs_DEMetro_Z |
1
|
-23.709
|
1.56e-20
|
-4.329
|
| HMC_vs_DEMetro_Z |
2
|
-25.517
|
2.03e-21
|
-4.659
|
| HMC_vs_DEMetro_Z |
3
|
-36.324
|
9.85e-26
|
-6.632
|
| HMC_vs_DEMetro_Z |
4
|
-41.672
|
1.97e-27
|
-7.608
|
| HMC_vs_DEMetro_Z |
5
|
-27.505
|
2.51e-22
|
-5.022
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.113 |
0.015 |
0.001 |
65.153 |
| HMC |
2.5 |
0.059 |
0.015 |
0.001 |
34.880 |
| HMC |
3.0 |
0.051 |
0.015 |
0.001 |
28.382 |
| HMC |
4.0 |
0.021 |
0.015 |
0.001 |
4.505 |
| HMC |
10.0 |
0.015 |
0.014 |
0.001 |
0.975 |
| HMC |
50.0 |
0.013 |
0.014 |
0.001 |
-0.296 |
| SMC |
2.1 |
0.405 |
0.015 |
0.001 |
259.847 |
| SMC |
2.5 |
0.412 |
0.015 |
0.001 |
313.107 |
| SMC |
3.0 |
0.419 |
0.015 |
0.001 |
318.585 |
| SMC |
4.0 |
0.413 |
0.015 |
0.001 |
304.653 |
| SMC |
10.0 |
0.377 |
0.014 |
0.001 |
280.634 |
| SMC |
50.0 |
0.097 |
0.014 |
0.001 |
72.818 |
| Metro |
2.1 |
0.146 |
0.015 |
0.001 |
87.212 |
| Metro |
2.5 |
0.082 |
0.015 |
0.001 |
52.644 |
| Metro |
3.0 |
0.055 |
0.015 |
0.001 |
31.868 |
| Metro |
4.0 |
0.038 |
0.015 |
0.001 |
17.313 |
| Metro |
10.0 |
0.029 |
0.014 |
0.001 |
11.751 |
| Metro |
50.0 |
0.024 |
0.014 |
0.001 |
9.281 |
| DEMetro_Z |
2.1 |
0.544 |
0.015 |
0.001 |
352.755 |
| DEMetro_Z |
2.5 |
0.513 |
0.015 |
0.001 |
392.751 |
| DEMetro_Z |
3.0 |
0.462 |
0.015 |
0.001 |
352.584 |
| DEMetro_Z |
4.0 |
0.400 |
0.015 |
0.001 |
294.440 |
| DEMetro_Z |
10.0 |
0.395 |
0.014 |
0.001 |
294.646 |
| DEMetro_Z |
50.0 |
0.301 |
0.014 |
0.001 |
250.495 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Correlation
(MvStudentT,
nu,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.705 |
0.0944 |
0.569 |
| HMC |
2.5 |
3.108 |
0.00341 |
1.332 |
| HMC |
3.0 |
2.990 |
0.00488 |
1.480 |
| HMC |
4.0 |
1.707 |
0.0933 |
0.487 |
| HMC |
10.0 |
4.318 |
8.55e-05 |
1.639 |
| HMC |
50.0 |
2.442 |
0.0184 |
0.876 |
| SMC |
2.1 |
-0.386 |
0.701 |
-0.094 |
| SMC |
2.5 |
1.340 |
0.186 |
0.442 |
| SMC |
3.0 |
-0.450 |
0.655 |
-0.119 |
| SMC |
4.0 |
0.281 |
0.779 |
0.067 |
| SMC |
10.0 |
0.386 |
0.701 |
0.112 |
| SMC |
50.0 |
-1.288 |
0.204 |
-0.284 |
| Metro |
2.1 |
4.731 |
4.78e-05 |
5.360 |
| Metro |
2.5 |
5.105 |
1.8e-05 |
9.271 |
| Metro |
3.0 |
6.703 |
2.08e-07 |
10.865 |
| Metro |
4.0 |
5.566 |
4.56e-06 |
6.822 |
| Metro |
10.0 |
6.376 |
5.25e-07 |
12.145 |
| Metro |
50.0 |
6.312 |
5.04e-07 |
6.246 |
| DEMetro_Z |
2.1 |
3.904 |
0.00045 |
3.004 |
| DEMetro_Z |
2.5 |
2.559 |
0.0159 |
5.054 |
| DEMetro_Z |
3.0 |
3.568 |
0.00106 |
2.095 |
| DEMetro_Z |
4.0 |
3.750 |
0.000532 |
1.552 |
| DEMetro_Z |
10.0 |
4.341 |
0.000108 |
2.330 |
| DEMetro_Z |
50.0 |
3.498 |
0.00102 |
1.227 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.110
|
0.00417
|
-0.568
|
| HMC_vs_DEMetro_Z |
1
|
-1.804
|
0.0816
|
-0.329
|
| HMC_vs_DEMetro_Z |
2
|
-0.945
|
0.352
|
-0.173
|
| HMC_vs_DEMetro_Z |
3
|
-2.287
|
0.0297
|
-0.418
|
| HMC_vs_DEMetro_Z |
4
|
-1.480
|
0.15
|
-0.270
|
| HMC_vs_DEMetro_Z |
5
|
-0.749
|
0.46
|
-0.137
|
| Metro_vs_SMC |
0
|
4.826
|
4.11e-05
|
0.881
|
| Metro_vs_SMC |
1
|
4.927
|
3.11e-05
|
0.900
|
| Metro_vs_SMC |
2
|
6.525
|
3.81e-07
|
1.191
|
| Metro_vs_SMC |
3
|
5.406
|
8.2e-06
|
0.987
|
| Metro_vs_SMC |
4
|
6.318
|
6.69e-07
|
1.153
|
| Metro_vs_SMC |
5
|
6.409
|
5.23e-07
|
1.170
|
| Metro_vs_DEMetro_Z |
0
|
1.669
|
0.106
|
0.305
|
| Metro_vs_DEMetro_Z |
1
|
1.526
|
0.138
|
0.279
|
| Metro_vs_DEMetro_Z |
2
|
5.064
|
2.13e-05
|
0.924
|
| Metro_vs_DEMetro_Z |
3
|
4.214
|
0.000223
|
0.769
|
| Metro_vs_DEMetro_Z |
4
|
4.806
|
4.35e-05
|
0.877
|
| Metro_vs_DEMetro_Z |
5
|
5.408
|
8.17e-06
|
0.987
|
| HMC_vs_Metro |
0
|
-4.325
|
0.000164
|
-0.790
|
| HMC_vs_Metro |
1
|
-4.273
|
0.00019
|
-0.780
|
| HMC_vs_Metro |
2
|
-5.265
|
1.22e-05
|
-0.961
|
| HMC_vs_Metro |
3
|
-5.292
|
1.13e-05
|
-0.966
|
| HMC_vs_Metro |
4
|
-5.327
|
1.02e-05
|
-0.973
|
| HMC_vs_Metro |
5
|
-5.048
|
2.22e-05
|
-0.922
|
| HMC_vs_SMC |
0
|
2.255
|
0.0318
|
0.412
|
| HMC_vs_SMC |
1
|
2.019
|
0.0528
|
0.369
|
| HMC_vs_SMC |
2
|
3.235
|
0.00303
|
0.591
|
| HMC_vs_SMC |
3
|
1.563
|
0.129
|
0.285
|
| HMC_vs_SMC |
4
|
3.674
|
0.000961
|
0.671
|
| HMC_vs_SMC |
5
|
3.762
|
0.00076
|
0.687
|
| DEMetro_Z_vs_SMC |
0
|
4.188
|
0.00024
|
0.765
|
| DEMetro_Z_vs_SMC |
1
|
2.273
|
0.0306
|
0.415
|
| DEMetro_Z_vs_SMC |
2
|
3.737
|
0.000813
|
0.682
|
| DEMetro_Z_vs_SMC |
3
|
3.599
|
0.00118
|
0.657
|
| DEMetro_Z_vs_SMC |
4
|
3.752
|
0.000782
|
0.685
|
| DEMetro_Z_vs_SMC |
5
|
4.863
|
3.71e-05
|
0.888
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.087 |
0.062 |
0.045 |
0.569 |
| HMC |
2.5 |
0.066 |
0.035 |
0.023 |
1.332 |
| HMC |
3.0 |
0.066 |
0.034 |
0.022 |
1.480 |
| HMC |
4.0 |
0.039 |
0.027 |
0.024 |
0.487 |
| HMC |
10.0 |
0.033 |
0.016 |
0.010 |
1.639 |
| HMC |
50.0 |
0.036 |
0.021 |
0.017 |
0.876 |
| SMC |
2.1 |
0.058 |
0.062 |
0.045 |
-0.094 |
| SMC |
2.5 |
0.045 |
0.035 |
0.023 |
0.442 |
| SMC |
3.0 |
0.031 |
0.034 |
0.022 |
-0.119 |
| SMC |
4.0 |
0.029 |
0.027 |
0.024 |
0.067 |
| SMC |
10.0 |
0.017 |
0.016 |
0.010 |
0.112 |
| SMC |
50.0 |
0.016 |
0.021 |
0.017 |
-0.284 |
| Metro |
2.1 |
0.301 |
0.062 |
0.045 |
5.360 |
| Metro |
2.5 |
0.249 |
0.035 |
0.023 |
9.271 |
| Metro |
3.0 |
0.272 |
0.034 |
0.022 |
10.865 |
| Metro |
4.0 |
0.188 |
0.027 |
0.024 |
6.822 |
| Metro |
10.0 |
0.142 |
0.016 |
0.010 |
12.145 |
| Metro |
50.0 |
0.124 |
0.021 |
0.017 |
6.246 |
| DEMetro_Z |
2.1 |
0.196 |
0.062 |
0.045 |
3.004 |
| DEMetro_Z |
2.5 |
0.152 |
0.035 |
0.023 |
5.054 |
| DEMetro_Z |
3.0 |
0.079 |
0.034 |
0.022 |
2.095 |
| DEMetro_Z |
4.0 |
0.064 |
0.027 |
0.024 |
1.552 |
| DEMetro_Z |
10.0 |
0.040 |
0.016 |
0.010 |
2.330 |
| DEMetro_Z |
50.0 |
0.041 |
0.021 |
0.017 |
1.227 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.132 |
0.265 |
-0.223 |
| HMC |
2.5 |
1.499 |
0.142 |
0.656 |
| HMC |
3.0 |
1.949 |
0.0595 |
1.190 |
| HMC |
4.0 |
3.060 |
0.00413 |
1.625 |
| HMC |
10.0 |
2.047 |
0.0471 |
0.884 |
| HMC |
50.0 |
2.193 |
0.0333 |
0.787 |
| SMC |
2.1 |
-1.900 |
0.0662 |
-0.358 |
| SMC |
2.5 |
-0.369 |
0.714 |
-0.142 |
| SMC |
3.0 |
-0.026 |
0.979 |
-0.006 |
| SMC |
4.0 |
-0.969 |
0.336 |
-0.252 |
| SMC |
10.0 |
0.302 |
0.763 |
0.081 |
| SMC |
50.0 |
0.027 |
0.979 |
0.007 |
| Metro |
2.1 |
-0.494 |
0.624 |
-0.104 |
| Metro |
2.5 |
1.306 |
0.197 |
0.379 |
| Metro |
3.0 |
2.531 |
0.0141 |
0.620 |
| Metro |
4.0 |
4.411 |
0.00012 |
5.379 |
| Metro |
10.0 |
6.177 |
7.88e-07 |
6.961 |
| Metro |
50.0 |
5.952 |
1e-06 |
3.877 |
| DEMetro_Z |
2.1 |
-0.950 |
0.349 |
-0.183 |
| DEMetro_Z |
2.5 |
0.831 |
0.412 |
0.507 |
| DEMetro_Z |
3.0 |
1.570 |
0.122 |
0.351 |
| DEMetro_Z |
4.0 |
4.755 |
2.49e-05 |
2.079 |
| DEMetro_Z |
10.0 |
4.077 |
0.000222 |
1.977 |
| DEMetro_Z |
50.0 |
3.060 |
0.0034 |
0.874 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.573
|
0.0155
|
0.470
|
| HMC_vs_SMC |
1
|
1.475
|
0.151
|
0.269
|
| HMC_vs_SMC |
2
|
2.064
|
0.0481
|
0.377
|
| HMC_vs_SMC |
3
|
4.358
|
0.00015
|
0.796
|
| HMC_vs_SMC |
4
|
1.920
|
0.0648
|
0.350
|
| HMC_vs_SMC |
5
|
2.047
|
0.0498
|
0.374
|
| Metro_vs_DEMetro_Z |
0
|
0.700
|
0.49
|
0.128
|
| Metro_vs_DEMetro_Z |
1
|
-0.199
|
0.843
|
-0.036
|
| Metro_vs_DEMetro_Z |
2
|
1.295
|
0.206
|
0.236
|
| Metro_vs_DEMetro_Z |
3
|
2.537
|
0.0168
|
0.463
|
| Metro_vs_DEMetro_Z |
4
|
4.521
|
9.59e-05
|
0.825
|
| Metro_vs_DEMetro_Z |
5
|
4.390
|
0.000138
|
0.801
|
| HMC_vs_Metro |
0
|
-1.053
|
0.301
|
-0.192
|
| HMC_vs_Metro |
1
|
0.758
|
0.455
|
0.138
|
| HMC_vs_Metro |
2
|
1.095
|
0.283
|
0.200
|
| HMC_vs_Metro |
3
|
-2.824
|
0.00849
|
-0.516
|
| HMC_vs_Metro |
4
|
-4.939
|
3.01e-05
|
-0.902
|
| HMC_vs_Metro |
5
|
-4.090
|
0.000313
|
-0.747
|
| HMC_vs_DEMetro_Z |
0
|
-0.867
|
0.393
|
-0.158
|
| HMC_vs_DEMetro_Z |
1
|
0.205
|
0.839
|
0.037
|
| HMC_vs_DEMetro_Z |
2
|
1.431
|
0.163
|
0.261
|
| HMC_vs_DEMetro_Z |
3
|
-0.695
|
0.492
|
-0.127
|
| HMC_vs_DEMetro_Z |
4
|
-2.114
|
0.0433
|
-0.386
|
| HMC_vs_DEMetro_Z |
5
|
-0.223
|
0.825
|
-0.041
|
| Metro_vs_SMC |
0
|
2.489
|
0.0188
|
0.454
|
| Metro_vs_SMC |
1
|
1.256
|
0.219
|
0.229
|
| Metro_vs_SMC |
2
|
3.317
|
0.00246
|
0.606
|
| Metro_vs_SMC |
3
|
4.674
|
6.28e-05
|
0.853
|
| Metro_vs_SMC |
4
|
6.200
|
9.21e-07
|
1.132
|
| Metro_vs_SMC |
5
|
5.491
|
6.49e-06
|
1.002
|
| DEMetro_Z_vs_SMC |
0
|
3.865
|
0.000576
|
0.706
|
| DEMetro_Z_vs_SMC |
1
|
0.924
|
0.363
|
0.169
|
| DEMetro_Z_vs_SMC |
2
|
4.553
|
8.78e-05
|
0.831
|
| DEMetro_Z_vs_SMC |
3
|
5.674
|
3.91e-06
|
1.036
|
| DEMetro_Z_vs_SMC |
4
|
3.516
|
0.00146
|
0.642
|
| DEMetro_Z_vs_SMC |
5
|
3.082
|
0.00447
|
0.563
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
4.442 |
7.653 |
14.425 |
-0.223 |
| HMC |
2.5 |
2.313 |
1.426 |
1.353 |
0.656 |
| HMC |
3.0 |
1.527 |
0.472 |
0.886 |
1.190 |
| HMC |
4.0 |
0.290 |
0.142 |
0.091 |
1.625 |
| HMC |
10.0 |
0.058 |
0.037 |
0.023 |
0.884 |
| HMC |
50.0 |
0.047 |
0.030 |
0.022 |
0.787 |
| SMC |
2.1 |
2.484 |
7.653 |
14.425 |
-0.358 |
| SMC |
2.5 |
1.234 |
1.426 |
1.353 |
-0.142 |
| SMC |
3.0 |
0.467 |
0.472 |
0.886 |
-0.006 |
| SMC |
4.0 |
0.119 |
0.142 |
0.091 |
-0.252 |
| SMC |
10.0 |
0.039 |
0.037 |
0.023 |
0.081 |
| SMC |
50.0 |
0.030 |
0.030 |
0.022 |
0.007 |
| Metro |
2.1 |
6.150 |
7.653 |
14.425 |
-0.104 |
| Metro |
2.5 |
1.938 |
1.426 |
1.353 |
0.379 |
| Metro |
3.0 |
1.022 |
0.472 |
0.886 |
0.620 |
| Metro |
4.0 |
0.634 |
0.142 |
0.091 |
5.379 |
| Metro |
10.0 |
0.199 |
0.037 |
0.023 |
6.961 |
| Metro |
50.0 |
0.115 |
0.030 |
0.022 |
3.877 |
| DEMetro_Z |
2.1 |
5.008 |
7.653 |
14.425 |
-0.183 |
| DEMetro_Z |
2.5 |
2.111 |
1.426 |
1.353 |
0.507 |
| DEMetro_Z |
3.0 |
0.783 |
0.472 |
0.886 |
0.351 |
| DEMetro_Z |
4.0 |
0.332 |
0.142 |
0.091 |
2.079 |
| DEMetro_Z |
10.0 |
0.083 |
0.037 |
0.023 |
1.977 |
| DEMetro_Z |
50.0 |
0.049 |
0.030 |
0.022 |
0.874 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.030 |
0.000185 |
1.306 |
| HMC |
2.5 |
4.366 |
0.000123 |
3.544 |
| HMC |
3.0 |
3.519 |
0.00133 |
3.019 |
| HMC |
4.0 |
5.533 |
1.13e-06 |
1.827 |
| HMC |
10.0 |
6.199 |
2.37e-07 |
2.736 |
| HMC |
50.0 |
3.327 |
0.00185 |
1.409 |
| SMC |
2.1 |
-1.413 |
0.164 |
-0.311 |
| SMC |
2.5 |
-1.248 |
0.218 |
-0.404 |
| SMC |
3.0 |
-0.514 |
0.609 |
-0.126 |
| SMC |
4.0 |
0.396 |
0.693 |
0.104 |
| SMC |
10.0 |
0.705 |
0.484 |
0.225 |
| SMC |
50.0 |
-1.671 |
0.101 |
-0.378 |
| Metro |
2.1 |
7.302 |
3.76e-08 |
9.263 |
| Metro |
2.5 |
8.564 |
1.66e-09 |
15.485 |
| Metro |
3.0 |
10.767 |
8.53e-12 |
16.568 |
| Metro |
4.0 |
9.629 |
1.06e-10 |
12.970 |
| Metro |
10.0 |
9.366 |
2.52e-10 |
21.200 |
| Metro |
50.0 |
7.931 |
6.62e-09 |
9.048 |
| DEMetro_Z |
2.1 |
6.740 |
1.34e-07 |
5.738 |
| DEMetro_Z |
2.5 |
3.398 |
0.00196 |
7.135 |
| DEMetro_Z |
3.0 |
7.011 |
3.76e-08 |
4.197 |
| DEMetro_Z |
4.0 |
8.301 |
2.59e-10 |
3.600 |
| DEMetro_Z |
10.0 |
7.336 |
1.74e-08 |
4.830 |
| DEMetro_Z |
50.0 |
5.899 |
3.67e-07 |
2.087 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
2.253
|
0.032
|
0.411
|
| Metro_vs_DEMetro_Z |
1
|
3.012
|
0.00534
|
0.550
|
| Metro_vs_DEMetro_Z |
2
|
7.113
|
7.93e-08
|
1.299
|
| Metro_vs_DEMetro_Z |
3
|
6.565
|
3.42e-07
|
1.199
|
| Metro_vs_DEMetro_Z |
4
|
6.473
|
4.39e-07
|
1.182
|
| Metro_vs_DEMetro_Z |
5
|
6.666
|
2.61e-07
|
1.217
|
| DEMetro_Z_vs_SMC |
0
|
7.246
|
5.59e-08
|
1.323
|
| DEMetro_Z_vs_SMC |
1
|
3.529
|
0.00141
|
0.644
|
| DEMetro_Z_vs_SMC |
2
|
7.354
|
4.22e-08
|
1.343
|
| DEMetro_Z_vs_SMC |
3
|
7.713
|
1.66e-08
|
1.408
|
| DEMetro_Z_vs_SMC |
4
|
6.685
|
2.48e-07
|
1.220
|
| DEMetro_Z_vs_SMC |
5
|
7.504
|
2.85e-08
|
1.370
|
| HMC_vs_DEMetro_Z |
0
|
-5.611
|
4.65e-06
|
-1.025
|
| HMC_vs_DEMetro_Z |
1
|
-1.625
|
0.115
|
-0.297
|
| HMC_vs_DEMetro_Z |
2
|
-1.302
|
0.203
|
-0.238
|
| HMC_vs_DEMetro_Z |
3
|
-3.286
|
0.00266
|
-0.600
|
| HMC_vs_DEMetro_Z |
4
|
-3.265
|
0.00281
|
-0.596
|
| HMC_vs_DEMetro_Z |
5
|
-1.343
|
0.19
|
-0.245
|
| HMC_vs_Metro |
0
|
-6.582
|
3.27e-07
|
-1.202
|
| HMC_vs_Metro |
1
|
-7.087
|
8.5e-08
|
-1.294
|
| HMC_vs_Metro |
2
|
-7.292
|
4.96e-08
|
-1.331
|
| HMC_vs_Metro |
3
|
-8.110
|
6.07e-09
|
-1.481
|
| HMC_vs_Metro |
4
|
-7.900
|
1.03e-08
|
-1.442
|
| HMC_vs_Metro |
5
|
-6.215
|
8.85e-07
|
-1.135
|
| HMC_vs_SMC |
0
|
5.706
|
3.58e-06
|
1.042
|
| HMC_vs_SMC |
1
|
4.737
|
5.26e-05
|
0.865
|
| HMC_vs_SMC |
2
|
3.650
|
0.00102
|
0.666
|
| HMC_vs_SMC |
3
|
6.056
|
1.37e-06
|
1.106
|
| HMC_vs_SMC |
4
|
4.808
|
4.33e-05
|
0.878
|
| HMC_vs_SMC |
5
|
5.046
|
2.23e-05
|
0.921
|
| Metro_vs_SMC |
0
|
7.479
|
3.04e-08
|
1.366
|
| Metro_vs_SMC |
1
|
8.833
|
1.02e-09
|
1.613
|
| Metro_vs_SMC |
2
|
11.026
|
6.88e-12
|
2.013
|
| Metro_vs_SMC |
3
|
9.375
|
2.79e-10
|
1.712
|
| Metro_vs_SMC |
4
|
9.018
|
6.53e-10
|
1.646
|
| Metro_vs_SMC |
5
|
8.125
|
5.84e-09
|
1.483
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.169 |
0.117 |
0.040 |
1.306 |
| HMC |
2.5 |
0.143 |
0.083 |
0.017 |
3.544 |
| HMC |
3.0 |
0.109 |
0.063 |
0.015 |
3.019 |
| HMC |
4.0 |
0.073 |
0.045 |
0.015 |
1.827 |
| HMC |
10.0 |
0.046 |
0.029 |
0.006 |
2.736 |
| HMC |
50.0 |
0.045 |
0.030 |
0.011 |
1.409 |
| SMC |
2.1 |
0.104 |
0.117 |
0.040 |
-0.311 |
| SMC |
2.5 |
0.076 |
0.083 |
0.017 |
-0.404 |
| SMC |
3.0 |
0.061 |
0.063 |
0.015 |
-0.126 |
| SMC |
4.0 |
0.047 |
0.045 |
0.015 |
0.104 |
| SMC |
10.0 |
0.030 |
0.029 |
0.006 |
0.225 |
| SMC |
50.0 |
0.026 |
0.030 |
0.011 |
-0.378 |
| Metro |
2.1 |
0.487 |
0.117 |
0.040 |
9.263 |
| Metro |
2.5 |
0.346 |
0.083 |
0.017 |
15.485 |
| Metro |
3.0 |
0.319 |
0.063 |
0.015 |
16.568 |
| Metro |
4.0 |
0.242 |
0.045 |
0.015 |
12.970 |
| Metro |
10.0 |
0.161 |
0.029 |
0.006 |
21.200 |
| Metro |
50.0 |
0.127 |
0.030 |
0.011 |
9.048 |
| DEMetro_Z |
2.1 |
0.346 |
0.117 |
0.040 |
5.738 |
| DEMetro_Z |
2.5 |
0.204 |
0.083 |
0.017 |
7.135 |
| DEMetro_Z |
3.0 |
0.127 |
0.063 |
0.015 |
4.197 |
| DEMetro_Z |
4.0 |
0.100 |
0.045 |
0.015 |
3.600 |
| DEMetro_Z |
10.0 |
0.059 |
0.029 |
0.006 |
4.830 |
| DEMetro_Z |
50.0 |
0.053 |
0.030 |
0.011 |
2.087 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.990 |
1.04e-05 |
2.007 |
| HMC |
2.5 |
3.964 |
0.000308 |
1.894 |
| HMC |
3.0 |
3.146 |
0.00296 |
1.219 |
| HMC |
4.0 |
4.830 |
1.45e-05 |
1.709 |
| HMC |
10.0 |
5.183 |
4.32e-06 |
1.819 |
| HMC |
50.0 |
3.426 |
0.00132 |
1.311 |
| SMC |
2.1 |
0.798 |
0.428 |
0.213 |
| SMC |
2.5 |
-0.393 |
0.696 |
-0.103 |
| SMC |
3.0 |
-0.392 |
0.697 |
-0.094 |
| SMC |
4.0 |
0.939 |
0.352 |
0.271 |
| SMC |
10.0 |
-0.146 |
0.885 |
-0.041 |
| SMC |
50.0 |
-1.603 |
0.114 |
-0.388 |
| Metro |
2.1 |
11.199 |
2.99e-12 |
15.272 |
| Metro |
2.5 |
9.959 |
5.63e-11 |
16.822 |
| Metro |
3.0 |
9.510 |
1.41e-10 |
12.810 |
| Metro |
4.0 |
10.118 |
2.57e-11 |
10.552 |
| Metro |
10.0 |
10.118 |
3.38e-11 |
13.679 |
| Metro |
50.0 |
8.933 |
4.31e-10 |
8.758 |
| DEMetro_Z |
2.1 |
7.548 |
1.85e-08 |
8.752 |
| DEMetro_Z |
2.5 |
6.625 |
1.96e-07 |
6.024 |
| DEMetro_Z |
3.0 |
7.201 |
1.09e-08 |
3.340 |
| DEMetro_Z |
4.0 |
8.670 |
4.75e-11 |
3.421 |
| DEMetro_Z |
10.0 |
5.778 |
1.22e-06 |
2.957 |
| DEMetro_Z |
50.0 |
5.468 |
1.72e-06 |
1.977 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.454
|
3.25e-08
|
1.361
|
| DEMetro_Z_vs_SMC |
1
|
6.897
|
1.41e-07
|
1.259
|
| DEMetro_Z_vs_SMC |
2
|
7.838
|
1.21e-08
|
1.431
|
| DEMetro_Z_vs_SMC |
3
|
7.458
|
3.22e-08
|
1.362
|
| DEMetro_Z_vs_SMC |
4
|
5.864
|
2.31e-06
|
1.071
|
| DEMetro_Z_vs_SMC |
5
|
7.113
|
7.93e-08
|
1.299
|
| HMC_vs_Metro |
0
|
-10.361
|
2.93e-11
|
-1.892
|
| HMC_vs_Metro |
1
|
-8.602
|
1.79e-09
|
-1.570
|
| HMC_vs_Metro |
2
|
-7.948
|
9.14e-09
|
-1.451
|
| HMC_vs_Metro |
3
|
-8.475
|
2.44e-09
|
-1.547
|
| HMC_vs_Metro |
4
|
-8.315
|
3.64e-09
|
-1.518
|
| HMC_vs_Metro |
5
|
-7.139
|
7.4e-08
|
-1.303
|
| Metro_vs_DEMetro_Z |
0
|
3.552
|
0.00133
|
0.648
|
| Metro_vs_DEMetro_Z |
1
|
5.802
|
2.75e-06
|
1.059
|
| Metro_vs_DEMetro_Z |
2
|
7.165
|
6.91e-08
|
1.308
|
| Metro_vs_DEMetro_Z |
3
|
6.240
|
8.27e-07
|
1.139
|
| Metro_vs_DEMetro_Z |
4
|
7.236
|
5.74e-08
|
1.321
|
| Metro_vs_DEMetro_Z |
5
|
7.100
|
8.22e-08
|
1.296
|
| HMC_vs_SMC |
0
|
4.061
|
0.000339
|
0.741
|
| HMC_vs_SMC |
1
|
4.212
|
0.000224
|
0.769
|
| HMC_vs_SMC |
2
|
3.456
|
0.00171
|
0.631
|
| HMC_vs_SMC |
3
|
4.930
|
3.09e-05
|
0.900
|
| HMC_vs_SMC |
4
|
4.713
|
5.64e-05
|
0.860
|
| HMC_vs_SMC |
5
|
4.988
|
2.62e-05
|
0.911
|
| Metro_vs_SMC |
0
|
10.789
|
1.15e-11
|
1.970
|
| Metro_vs_SMC |
1
|
9.934
|
7.67e-11
|
1.814
|
| Metro_vs_SMC |
2
|
9.615
|
1.6e-10
|
1.755
|
| Metro_vs_SMC |
3
|
9.465
|
2.26e-10
|
1.728
|
| Metro_vs_SMC |
4
|
9.696
|
1.32e-10
|
1.770
|
| Metro_vs_SMC |
5
|
9.308
|
3.27e-10
|
1.699
|
| HMC_vs_DEMetro_Z |
0
|
-5.546
|
5.58e-06
|
-1.012
|
| HMC_vs_DEMetro_Z |
1
|
-4.195
|
0.000235
|
-0.766
|
| HMC_vs_DEMetro_Z |
2
|
-3.730
|
0.000828
|
-0.681
|
| HMC_vs_DEMetro_Z |
3
|
-3.514
|
0.00147
|
-0.641
|
| HMC_vs_DEMetro_Z |
4
|
-2.168
|
0.0385
|
-0.396
|
| HMC_vs_DEMetro_Z |
5
|
-1.355
|
0.186
|
-0.247
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.026 |
0.015 |
0.006 |
2.007 |
| HMC |
2.5 |
0.024 |
0.016 |
0.005 |
1.894 |
| HMC |
3.0 |
0.022 |
0.015 |
0.006 |
1.219 |
| HMC |
4.0 |
0.024 |
0.014 |
0.006 |
1.709 |
| HMC |
10.0 |
0.022 |
0.013 |
0.005 |
1.819 |
| HMC |
50.0 |
0.023 |
0.015 |
0.006 |
1.311 |
| SMC |
2.1 |
0.016 |
0.015 |
0.006 |
0.213 |
| SMC |
2.5 |
0.015 |
0.016 |
0.005 |
-0.103 |
| SMC |
3.0 |
0.015 |
0.015 |
0.006 |
-0.094 |
| SMC |
4.0 |
0.015 |
0.014 |
0.006 |
0.271 |
| SMC |
10.0 |
0.013 |
0.013 |
0.005 |
-0.041 |
| SMC |
50.0 |
0.013 |
0.015 |
0.006 |
-0.388 |
| Metro |
2.1 |
0.103 |
0.015 |
0.006 |
15.272 |
| Metro |
2.5 |
0.091 |
0.016 |
0.005 |
16.822 |
| Metro |
3.0 |
0.086 |
0.015 |
0.006 |
12.810 |
| Metro |
4.0 |
0.077 |
0.014 |
0.006 |
10.552 |
| Metro |
10.0 |
0.080 |
0.013 |
0.005 |
13.679 |
| Metro |
50.0 |
0.066 |
0.015 |
0.006 |
8.758 |
| DEMetro_Z |
2.1 |
0.065 |
0.015 |
0.006 |
8.752 |
| DEMetro_Z |
2.5 |
0.043 |
0.016 |
0.005 |
6.024 |
| DEMetro_Z |
3.0 |
0.034 |
0.015 |
0.006 |
3.340 |
| DEMetro_Z |
4.0 |
0.034 |
0.014 |
0.006 |
3.421 |
| DEMetro_Z |
10.0 |
0.028 |
0.013 |
0.005 |
2.957 |
| DEMetro_Z |
50.0 |
0.027 |
0.015 |
0.006 |
1.977 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.717 |
0.0938 |
0.790 |
| HMC |
2.5 |
2.502 |
0.0164 |
1.066 |
| HMC |
3.0 |
2.096 |
0.042 |
0.852 |
| HMC |
4.0 |
2.834 |
0.00673 |
1.003 |
| HMC |
10.0 |
3.119 |
0.00334 |
1.375 |
| HMC |
50.0 |
1.844 |
0.0719 |
0.708 |
| SMC |
2.1 |
-0.203 |
0.84 |
-0.051 |
| SMC |
2.5 |
0.579 |
0.565 |
0.184 |
| SMC |
3.0 |
-0.766 |
0.447 |
-0.193 |
| SMC |
4.0 |
-0.692 |
0.492 |
-0.147 |
| SMC |
10.0 |
-0.756 |
0.453 |
-0.185 |
| SMC |
50.0 |
-1.083 |
0.284 |
-0.241 |
| Metro |
2.1 |
6.378 |
3.37e-07 |
4.813 |
| Metro |
2.5 |
6.895 |
1.31e-07 |
14.481 |
| Metro |
3.0 |
6.401 |
4.39e-07 |
7.934 |
| Metro |
4.0 |
5.494 |
5.32e-06 |
5.789 |
| Metro |
10.0 |
6.857 |
1.33e-07 |
10.165 |
| Metro |
50.0 |
5.434 |
6.34e-06 |
5.806 |
| DEMetro_Z |
2.1 |
2.243 |
0.0297 |
0.821 |
| DEMetro_Z |
2.5 |
4.461 |
9.77e-05 |
4.086 |
| DEMetro_Z |
3.0 |
3.438 |
0.00151 |
1.972 |
| DEMetro_Z |
4.0 |
4.134 |
0.000167 |
1.733 |
| DEMetro_Z |
10.0 |
5.307 |
5.12e-06 |
2.634 |
| DEMetro_Z |
50.0 |
1.645 |
0.106 |
0.447 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.071
|
0.944
|
-0.013
|
| HMC_vs_DEMetro_Z |
1
|
-3.266
|
0.0028
|
-0.596
|
| HMC_vs_DEMetro_Z |
2
|
-1.830
|
0.0775
|
-0.334
|
| HMC_vs_DEMetro_Z |
3
|
-1.519
|
0.14
|
-0.277
|
| HMC_vs_DEMetro_Z |
4
|
-2.801
|
0.00899
|
-0.511
|
| HMC_vs_DEMetro_Z |
5
|
0.750
|
0.459
|
0.137
|
| Metro_vs_SMC |
0
|
6.321
|
6.62e-07
|
1.154
|
| Metro_vs_SMC |
1
|
6.483
|
4.28e-07
|
1.184
|
| Metro_vs_SMC |
2
|
6.615
|
3e-07
|
1.208
|
| Metro_vs_SMC |
3
|
5.624
|
4.49e-06
|
1.027
|
| Metro_vs_SMC |
4
|
7.155
|
7.1e-08
|
1.306
|
| Metro_vs_SMC |
5
|
5.719
|
3.45e-06
|
1.044
|
| Metro_vs_DEMetro_Z |
0
|
5.348
|
9.64e-06
|
0.976
|
| Metro_vs_DEMetro_Z |
1
|
4.788
|
4.57e-05
|
0.874
|
| Metro_vs_DEMetro_Z |
2
|
4.395
|
0.000136
|
0.802
|
| Metro_vs_DEMetro_Z |
3
|
3.592
|
0.0012
|
0.656
|
| Metro_vs_DEMetro_Z |
4
|
5.201
|
1.45e-05
|
0.950
|
| Metro_vs_DEMetro_Z |
5
|
4.946
|
2.95e-05
|
0.903
|
| HMC_vs_Metro |
0
|
-4.695
|
5.92e-05
|
-0.857
|
| HMC_vs_Metro |
1
|
-5.842
|
2.46e-06
|
-1.067
|
| HMC_vs_Metro |
2
|
-5.427
|
7.75e-06
|
-0.991
|
| HMC_vs_Metro |
3
|
-4.367
|
0.000147
|
-0.797
|
| HMC_vs_Metro |
4
|
-5.821
|
2.6e-06
|
-1.063
|
| HMC_vs_Metro |
5
|
-4.571
|
8.34e-05
|
-0.835
|
| HMC_vs_SMC |
0
|
1.774
|
0.0866
|
0.324
|
| HMC_vs_SMC |
1
|
1.883
|
0.0698
|
0.344
|
| HMC_vs_SMC |
2
|
3.469
|
0.00165
|
0.633
|
| HMC_vs_SMC |
3
|
3.205
|
0.00327
|
0.585
|
| HMC_vs_SMC |
4
|
3.542
|
0.00136
|
0.647
|
| HMC_vs_SMC |
5
|
2.508
|
0.018
|
0.458
|
| DEMetro_Z_vs_SMC |
0
|
2.241
|
0.0329
|
0.409
|
| DEMetro_Z_vs_SMC |
1
|
4.202
|
0.000231
|
0.767
|
| DEMetro_Z_vs_SMC |
2
|
3.854
|
0.000594
|
0.704
|
| DEMetro_Z_vs_SMC |
3
|
4.542
|
9.05e-05
|
0.829
|
| DEMetro_Z_vs_SMC |
4
|
5.753
|
3.15e-06
|
1.050
|
| DEMetro_Z_vs_SMC |
5
|
2.934
|
0.00648
|
0.536
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.097 |
0.062 |
0.045 |
0.790 |
| HMC |
2.5 |
0.060 |
0.035 |
0.023 |
1.066 |
| HMC |
3.0 |
0.052 |
0.034 |
0.022 |
0.852 |
| HMC |
4.0 |
0.051 |
0.027 |
0.024 |
1.003 |
| HMC |
10.0 |
0.030 |
0.016 |
0.010 |
1.375 |
| HMC |
50.0 |
0.033 |
0.021 |
0.017 |
0.708 |
| SMC |
2.1 |
0.060 |
0.062 |
0.045 |
-0.051 |
| SMC |
2.5 |
0.039 |
0.035 |
0.023 |
0.184 |
| SMC |
3.0 |
0.029 |
0.034 |
0.022 |
-0.193 |
| SMC |
4.0 |
0.024 |
0.027 |
0.024 |
-0.147 |
| SMC |
10.0 |
0.014 |
0.016 |
0.010 |
-0.185 |
| SMC |
50.0 |
0.017 |
0.021 |
0.017 |
-0.241 |
| Metro |
2.1 |
0.276 |
0.062 |
0.045 |
4.813 |
| Metro |
2.5 |
0.370 |
0.035 |
0.023 |
14.481 |
| Metro |
3.0 |
0.207 |
0.034 |
0.022 |
7.934 |
| Metro |
4.0 |
0.164 |
0.027 |
0.024 |
5.789 |
| Metro |
10.0 |
0.122 |
0.016 |
0.010 |
10.165 |
| Metro |
50.0 |
0.117 |
0.021 |
0.017 |
5.806 |
| DEMetro_Z |
2.1 |
0.099 |
0.062 |
0.045 |
0.821 |
| DEMetro_Z |
2.5 |
0.130 |
0.035 |
0.023 |
4.086 |
| DEMetro_Z |
3.0 |
0.077 |
0.034 |
0.022 |
1.972 |
| DEMetro_Z |
4.0 |
0.068 |
0.027 |
0.024 |
1.733 |
| DEMetro_Z |
10.0 |
0.043 |
0.016 |
0.010 |
2.634 |
| DEMetro_Z |
50.0 |
0.029 |
0.021 |
0.017 |
0.447 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.576 |
0.125 |
-0.293 |
| HMC |
2.5 |
1.021 |
0.314 |
0.453 |
| HMC |
3.0 |
1.108 |
0.273 |
0.251 |
| HMC |
4.0 |
2.009 |
0.051 |
0.832 |
| HMC |
10.0 |
3.350 |
0.00179 |
1.541 |
| HMC |
50.0 |
3.259 |
0.00219 |
1.312 |
| SMC |
2.1 |
-1.493 |
0.144 |
-0.288 |
| SMC |
2.5 |
-0.928 |
0.357 |
-0.244 |
| SMC |
3.0 |
0.134 |
0.894 |
0.028 |
| SMC |
4.0 |
0.664 |
0.509 |
0.173 |
| SMC |
10.0 |
0.012 |
0.99 |
0.003 |
| SMC |
50.0 |
-0.177 |
0.86 |
-0.046 |
| Metro |
2.1 |
-1.067 |
0.294 |
-0.202 |
| Metro |
2.5 |
1.473 |
0.146 |
0.394 |
| Metro |
3.0 |
3.223 |
0.00218 |
0.723 |
| Metro |
4.0 |
4.269 |
0.000171 |
4.127 |
| Metro |
10.0 |
6.007 |
1.26e-06 |
6.704 |
| Metro |
50.0 |
5.811 |
2.17e-06 |
6.259 |
| DEMetro_Z |
2.1 |
-1.220 |
0.231 |
-0.233 |
| DEMetro_Z |
2.5 |
1.119 |
0.268 |
0.310 |
| DEMetro_Z |
3.0 |
1.704 |
0.0941 |
0.396 |
| DEMetro_Z |
4.0 |
3.463 |
0.00127 |
1.522 |
| DEMetro_Z |
10.0 |
3.461 |
0.00152 |
2.591 |
| DEMetro_Z |
50.0 |
3.037 |
0.00389 |
1.091 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-0.075
|
0.941
|
-0.014
|
| HMC_vs_SMC |
1
|
1.526
|
0.138
|
0.279
|
| HMC_vs_SMC |
2
|
1.603
|
0.12
|
0.293
|
| HMC_vs_SMC |
3
|
1.550
|
0.132
|
0.283
|
| HMC_vs_SMC |
4
|
3.298
|
0.00258
|
0.602
|
| HMC_vs_SMC |
5
|
3.835
|
0.000625
|
0.700
|
| Metro_vs_DEMetro_Z |
0
|
1.369
|
0.182
|
0.250
|
| Metro_vs_DEMetro_Z |
1
|
0.365
|
0.718
|
0.067
|
| Metro_vs_DEMetro_Z |
2
|
1.876
|
0.0708
|
0.342
|
| Metro_vs_DEMetro_Z |
3
|
2.656
|
0.0127
|
0.485
|
| Metro_vs_DEMetro_Z |
4
|
2.764
|
0.00982
|
0.505
|
| Metro_vs_DEMetro_Z |
5
|
4.614
|
7.41e-05
|
0.842
|
| HMC_vs_Metro |
0
|
-1.804
|
0.0817
|
-0.329
|
| HMC_vs_Metro |
1
|
0.134
|
0.894
|
0.025
|
| HMC_vs_Metro |
2
|
-3.032
|
0.00508
|
-0.554
|
| HMC_vs_Metro |
3
|
-3.279
|
0.00271
|
-0.599
|
| HMC_vs_Metro |
4
|
-4.979
|
2.69e-05
|
-0.909
|
| HMC_vs_Metro |
5
|
-4.762
|
4.91e-05
|
-0.869
|
| HMC_vs_DEMetro_Z |
0
|
-1.013
|
0.319
|
-0.185
|
| HMC_vs_DEMetro_Z |
1
|
0.325
|
0.748
|
0.059
|
| HMC_vs_DEMetro_Z |
2
|
-0.919
|
0.366
|
-0.168
|
| HMC_vs_DEMetro_Z |
3
|
-1.186
|
0.245
|
-0.217
|
| HMC_vs_DEMetro_Z |
4
|
-1.279
|
0.211
|
-0.234
|
| HMC_vs_DEMetro_Z |
5
|
0.588
|
0.561
|
0.107
|
| Metro_vs_SMC |
0
|
2.330
|
0.027
|
0.425
|
| Metro_vs_SMC |
1
|
2.688
|
0.0118
|
0.491
|
| Metro_vs_SMC |
2
|
4.164
|
0.000256
|
0.760
|
| Metro_vs_SMC |
3
|
3.916
|
0.000503
|
0.715
|
| Metro_vs_SMC |
4
|
6.114
|
1.17e-06
|
1.116
|
| Metro_vs_SMC |
5
|
5.979
|
1.69e-06
|
1.092
|
| DEMetro_Z_vs_SMC |
0
|
1.282
|
0.21
|
0.234
|
| DEMetro_Z_vs_SMC |
1
|
2.643
|
0.0131
|
0.482
|
| DEMetro_Z_vs_SMC |
2
|
2.749
|
0.0102
|
0.502
|
| DEMetro_Z_vs_SMC |
3
|
2.837
|
0.00823
|
0.518
|
| DEMetro_Z_vs_SMC |
4
|
3.423
|
0.00187
|
0.625
|
| DEMetro_Z_vs_SMC |
5
|
3.643
|
0.00105
|
0.665
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
3.425 |
7.653 |
14.425 |
-0.293 |
| HMC |
2.5 |
2.039 |
1.426 |
1.353 |
0.453 |
| HMC |
3.0 |
0.695 |
0.472 |
0.886 |
0.251 |
| HMC |
4.0 |
0.218 |
0.142 |
0.091 |
0.832 |
| HMC |
10.0 |
0.073 |
0.037 |
0.023 |
1.541 |
| HMC |
50.0 |
0.059 |
0.030 |
0.022 |
1.312 |
| SMC |
2.1 |
3.497 |
7.653 |
14.425 |
-0.288 |
| SMC |
2.5 |
1.096 |
1.426 |
1.353 |
-0.244 |
| SMC |
3.0 |
0.497 |
0.472 |
0.886 |
0.028 |
| SMC |
4.0 |
0.158 |
0.142 |
0.091 |
0.173 |
| SMC |
10.0 |
0.037 |
0.037 |
0.023 |
0.003 |
| SMC |
50.0 |
0.029 |
0.030 |
0.022 |
-0.046 |
| Metro |
2.1 |
4.746 |
7.653 |
14.425 |
-0.202 |
| Metro |
2.5 |
1.959 |
1.426 |
1.353 |
0.394 |
| Metro |
3.0 |
1.113 |
0.472 |
0.886 |
0.723 |
| Metro |
4.0 |
0.519 |
0.142 |
0.091 |
4.127 |
| Metro |
10.0 |
0.193 |
0.037 |
0.023 |
6.704 |
| Metro |
50.0 |
0.167 |
0.030 |
0.022 |
6.259 |
| DEMetro_Z |
2.1 |
4.294 |
7.653 |
14.425 |
-0.233 |
| DEMetro_Z |
2.5 |
1.845 |
1.426 |
1.353 |
0.310 |
| DEMetro_Z |
3.0 |
0.823 |
0.472 |
0.886 |
0.396 |
| DEMetro_Z |
4.0 |
0.281 |
0.142 |
0.091 |
1.522 |
| DEMetro_Z |
10.0 |
0.097 |
0.037 |
0.023 |
2.591 |
| DEMetro_Z |
50.0 |
0.054 |
0.030 |
0.022 |
1.091 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.639 |
0.000861 |
2.076 |
| HMC |
2.5 |
4.462 |
7.93e-05 |
2.587 |
| HMC |
3.0 |
4.251 |
0.000139 |
2.224 |
| HMC |
4.0 |
5.179 |
5.01e-06 |
1.955 |
| HMC |
10.0 |
5.186 |
8.26e-06 |
2.793 |
| HMC |
50.0 |
2.896 |
0.00606 |
1.264 |
| SMC |
2.1 |
0.432 |
0.668 |
0.151 |
| SMC |
2.5 |
-1.395 |
0.169 |
-0.413 |
| SMC |
3.0 |
0.132 |
0.896 |
0.034 |
| SMC |
4.0 |
0.075 |
0.94 |
0.017 |
| SMC |
10.0 |
-0.635 |
0.528 |
-0.161 |
| SMC |
50.0 |
-1.640 |
0.107 |
-0.372 |
| Metro |
2.1 |
11.715 |
1.29e-13 |
7.098 |
| Metro |
2.5 |
9.890 |
7.1e-11 |
19.774 |
| Metro |
3.0 |
10.653 |
9.27e-12 |
13.335 |
| Metro |
4.0 |
8.274 |
3.03e-09 |
11.126 |
| Metro |
10.0 |
9.312 |
2.67e-10 |
16.876 |
| Metro |
50.0 |
6.788 |
1.55e-07 |
9.077 |
| DEMetro_Z |
2.1 |
8.587 |
3.7e-11 |
3.122 |
| DEMetro_Z |
2.5 |
6.892 |
9.1e-08 |
6.139 |
| DEMetro_Z |
3.0 |
8.181 |
7.88e-10 |
4.225 |
| DEMetro_Z |
4.0 |
7.454 |
3.61e-09 |
3.185 |
| DEMetro_Z |
10.0 |
8.504 |
6.09e-10 |
5.443 |
| DEMetro_Z |
50.0 |
5.229 |
2.44e-06 |
1.363 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
6.467
|
4.46e-07
|
1.181
|
| Metro_vs_DEMetro_Z |
1
|
6.317
|
6.69e-07
|
1.153
|
| Metro_vs_DEMetro_Z |
2
|
6.890
|
1.43e-07
|
1.258
|
| Metro_vs_DEMetro_Z |
3
|
5.876
|
2.24e-06
|
1.073
|
| Metro_vs_DEMetro_Z |
4
|
6.404
|
5.29e-07
|
1.169
|
| Metro_vs_DEMetro_Z |
5
|
5.822
|
2.6e-06
|
1.063
|
| DEMetro_Z_vs_SMC |
0
|
7.328
|
4.51e-08
|
1.338
|
| DEMetro_Z_vs_SMC |
1
|
8.103
|
6.17e-09
|
1.479
|
| DEMetro_Z_vs_SMC |
2
|
8.110
|
6.07e-09
|
1.481
|
| DEMetro_Z_vs_SMC |
3
|
7.656
|
1.93e-08
|
1.398
|
| DEMetro_Z_vs_SMC |
4
|
8.812
|
1.07e-09
|
1.609
|
| DEMetro_Z_vs_SMC |
5
|
7.896
|
1.04e-08
|
1.442
|
| HMC_vs_DEMetro_Z |
0
|
-1.914
|
0.0656
|
-0.349
|
| HMC_vs_DEMetro_Z |
1
|
-3.551
|
0.00133
|
-0.648
|
| HMC_vs_DEMetro_Z |
2
|
-3.079
|
0.00451
|
-0.562
|
| HMC_vs_DEMetro_Z |
3
|
-2.494
|
0.0186
|
-0.455
|
| HMC_vs_DEMetro_Z |
4
|
-3.766
|
0.000752
|
-0.688
|
| HMC_vs_DEMetro_Z |
5
|
-0.239
|
0.812
|
-0.044
|
| HMC_vs_Metro |
0
|
-6.122
|
1.14e-06
|
-1.118
|
| HMC_vs_Metro |
1
|
-7.635
|
2.03e-08
|
-1.394
|
| HMC_vs_Metro |
2
|
-8.627
|
1.68e-09
|
-1.575
|
| HMC_vs_Metro |
3
|
-7.008
|
1.05e-07
|
-1.280
|
| HMC_vs_Metro |
4
|
-7.356
|
4.2e-08
|
-1.343
|
| HMC_vs_Metro |
5
|
-5.570
|
5.21e-06
|
-1.017
|
| HMC_vs_SMC |
0
|
3.076
|
0.00455
|
0.562
|
| HMC_vs_SMC |
1
|
5.059
|
2.15e-05
|
0.924
|
| HMC_vs_SMC |
2
|
4.551
|
8.82e-05
|
0.831
|
| HMC_vs_SMC |
3
|
4.949
|
2.92e-05
|
0.904
|
| HMC_vs_SMC |
4
|
5.473
|
6.82e-06
|
0.999
|
| HMC_vs_SMC |
5
|
4.030
|
0.000369
|
0.736
|
| Metro_vs_SMC |
0
|
11.944
|
1.02e-12
|
2.181
|
| Metro_vs_SMC |
1
|
10.027
|
6.21e-11
|
1.831
|
| Metro_vs_SMC |
2
|
10.378
|
2.83e-11
|
1.895
|
| Metro_vs_SMC |
3
|
8.204
|
4.79e-09
|
1.498
|
| Metro_vs_SMC |
4
|
9.765
|
1.13e-10
|
1.783
|
| Metro_vs_SMC |
5
|
6.972
|
1.15e-07
|
1.273
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.200 |
0.117 |
0.040 |
2.076 |
| HMC |
2.5 |
0.127 |
0.083 |
0.017 |
2.587 |
| HMC |
3.0 |
0.097 |
0.063 |
0.015 |
2.224 |
| HMC |
4.0 |
0.075 |
0.045 |
0.015 |
1.955 |
| HMC |
10.0 |
0.046 |
0.029 |
0.006 |
2.793 |
| HMC |
50.0 |
0.044 |
0.030 |
0.011 |
1.264 |
| SMC |
2.1 |
0.123 |
0.117 |
0.040 |
0.151 |
| SMC |
2.5 |
0.076 |
0.083 |
0.017 |
-0.413 |
| SMC |
3.0 |
0.063 |
0.063 |
0.015 |
0.034 |
| SMC |
4.0 |
0.046 |
0.045 |
0.015 |
0.017 |
| SMC |
10.0 |
0.028 |
0.029 |
0.006 |
-0.161 |
| SMC |
50.0 |
0.026 |
0.030 |
0.011 |
-0.372 |
| Metro |
2.1 |
0.401 |
0.117 |
0.040 |
7.098 |
| Metro |
2.5 |
0.419 |
0.083 |
0.017 |
19.774 |
| Metro |
3.0 |
0.269 |
0.063 |
0.015 |
13.335 |
| Metro |
4.0 |
0.214 |
0.045 |
0.015 |
11.126 |
| Metro |
10.0 |
0.134 |
0.029 |
0.006 |
16.876 |
| Metro |
50.0 |
0.128 |
0.030 |
0.011 |
9.077 |
| DEMetro_Z |
2.1 |
0.242 |
0.117 |
0.040 |
3.122 |
| DEMetro_Z |
2.5 |
0.187 |
0.083 |
0.017 |
6.139 |
| DEMetro_Z |
3.0 |
0.128 |
0.063 |
0.015 |
4.225 |
| DEMetro_Z |
4.0 |
0.093 |
0.045 |
0.015 |
3.185 |
| DEMetro_Z |
10.0 |
0.063 |
0.029 |
0.006 |
5.443 |
| DEMetro_Z |
50.0 |
0.045 |
0.030 |
0.011 |
1.363 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.396 |
0.023 |
3.700 |
| HMC |
2.5 |
4.143 |
0.00017 |
1.832 |
| HMC |
3.0 |
4.307 |
9.08e-05 |
1.676 |
| HMC |
4.0 |
5.334 |
2.24e-06 |
1.747 |
| HMC |
10.0 |
4.162 |
0.000154 |
1.761 |
| HMC |
50.0 |
3.167 |
0.00293 |
1.397 |
| SMC |
2.1 |
1.428 |
0.16 |
0.512 |
| SMC |
2.5 |
-0.229 |
0.819 |
-0.066 |
| SMC |
3.0 |
-0.342 |
0.733 |
-0.091 |
| SMC |
4.0 |
0.574 |
0.568 |
0.150 |
| SMC |
10.0 |
-0.642 |
0.523 |
-0.157 |
| SMC |
50.0 |
-1.956 |
0.0553 |
-0.484 |
| Metro |
2.1 |
10.476 |
1.27e-11 |
12.060 |
| Metro |
2.5 |
9.309 |
2.78e-10 |
18.688 |
| Metro |
3.0 |
8.543 |
1.54e-09 |
11.579 |
| Metro |
4.0 |
8.965 |
4.76e-10 |
10.436 |
| Metro |
10.0 |
7.831 |
9.29e-09 |
10.045 |
| Metro |
50.0 |
7.514 |
2.03e-08 |
8.736 |
| DEMetro_Z |
2.1 |
8.072 |
1.99e-09 |
5.132 |
| DEMetro_Z |
2.5 |
8.666 |
1.72e-10 |
4.369 |
| DEMetro_Z |
3.0 |
7.754 |
1.04e-09 |
3.114 |
| DEMetro_Z |
4.0 |
6.248 |
1.45e-07 |
2.441 |
| DEMetro_Z |
10.0 |
7.327 |
6.23e-09 |
3.246 |
| DEMetro_Z |
50.0 |
4.428 |
4.34e-05 |
1.214 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.654
|
1.94e-08
|
1.397
|
| DEMetro_Z_vs_SMC |
1
|
9.188
|
4.34e-10
|
1.678
|
| DEMetro_Z_vs_SMC |
2
|
7.663
|
1.89e-08
|
1.399
|
| DEMetro_Z_vs_SMC |
3
|
5.635
|
4.35e-06
|
1.029
|
| DEMetro_Z_vs_SMC |
4
|
7.794
|
1.35e-08
|
1.423
|
| DEMetro_Z_vs_SMC |
5
|
6.411
|
5.19e-07
|
1.171
|
| HMC_vs_Metro |
0
|
-4.028
|
0.000371
|
-0.735
|
| HMC_vs_Metro |
1
|
-8.170
|
5.23e-09
|
-1.492
|
| HMC_vs_Metro |
2
|
-7.167
|
6.88e-08
|
-1.309
|
| HMC_vs_Metro |
3
|
-7.804
|
1.32e-08
|
-1.425
|
| HMC_vs_Metro |
4
|
-5.895
|
2.12e-06
|
-1.076
|
| HMC_vs_Metro |
5
|
-6.126
|
1.13e-06
|
-1.119
|
| Metro_vs_DEMetro_Z |
0
|
5.158
|
1.64e-05
|
0.942
|
| Metro_vs_DEMetro_Z |
1
|
6.974
|
1.15e-07
|
1.273
|
| Metro_vs_DEMetro_Z |
2
|
6.353
|
6.08e-07
|
1.160
|
| Metro_vs_DEMetro_Z |
3
|
6.729
|
2.2e-07
|
1.228
|
| Metro_vs_DEMetro_Z |
4
|
5.174
|
1.56e-05
|
0.945
|
| Metro_vs_DEMetro_Z |
5
|
6.938
|
1.26e-07
|
1.267
|
| HMC_vs_SMC |
0
|
2.081
|
0.0463
|
0.380
|
| HMC_vs_SMC |
1
|
4.667
|
6.39e-05
|
0.852
|
| HMC_vs_SMC |
2
|
4.510
|
9.87e-05
|
0.823
|
| HMC_vs_SMC |
3
|
4.664
|
6.46e-05
|
0.851
|
| HMC_vs_SMC |
4
|
4.836
|
4e-05
|
0.883
|
| HMC_vs_SMC |
5
|
4.695
|
5.92e-05
|
0.857
|
| Metro_vs_SMC |
0
|
10.318
|
3.23e-11
|
1.884
|
| Metro_vs_SMC |
1
|
9.475
|
2.21e-10
|
1.730
|
| Metro_vs_SMC |
2
|
8.611
|
1.75e-09
|
1.572
|
| Metro_vs_SMC |
3
|
8.583
|
1.87e-09
|
1.567
|
| Metro_vs_SMC |
4
|
8.310
|
3.68e-09
|
1.517
|
| Metro_vs_SMC |
5
|
7.710
|
1.68e-08
|
1.408
|
| HMC_vs_DEMetro_Z |
0
|
-0.847
|
0.404
|
-0.155
|
| HMC_vs_DEMetro_Z |
1
|
-4.274
|
0.000189
|
-0.780
|
| HMC_vs_DEMetro_Z |
2
|
-2.890
|
0.00722
|
-0.528
|
| HMC_vs_DEMetro_Z |
3
|
-1.525
|
0.138
|
-0.278
|
| HMC_vs_DEMetro_Z |
4
|
-3.003
|
0.00546
|
-0.548
|
| HMC_vs_DEMetro_Z |
5
|
0.425
|
0.674
|
0.078
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.036 |
0.015 |
0.006 |
3.700 |
| HMC |
2.5 |
0.024 |
0.016 |
0.005 |
1.832 |
| HMC |
3.0 |
0.024 |
0.015 |
0.006 |
1.676 |
| HMC |
4.0 |
0.024 |
0.014 |
0.006 |
1.747 |
| HMC |
10.0 |
0.022 |
0.013 |
0.005 |
1.761 |
| HMC |
50.0 |
0.023 |
0.015 |
0.006 |
1.397 |
| SMC |
2.1 |
0.018 |
0.015 |
0.006 |
0.512 |
| SMC |
2.5 |
0.015 |
0.016 |
0.005 |
-0.066 |
| SMC |
3.0 |
0.015 |
0.015 |
0.006 |
-0.091 |
| SMC |
4.0 |
0.015 |
0.014 |
0.006 |
0.150 |
| SMC |
10.0 |
0.012 |
0.013 |
0.005 |
-0.157 |
| SMC |
50.0 |
0.012 |
0.015 |
0.006 |
-0.484 |
| Metro |
2.1 |
0.084 |
0.015 |
0.006 |
12.060 |
| Metro |
2.5 |
0.100 |
0.016 |
0.005 |
18.688 |
| Metro |
3.0 |
0.079 |
0.015 |
0.006 |
11.579 |
| Metro |
4.0 |
0.076 |
0.014 |
0.006 |
10.436 |
| Metro |
10.0 |
0.062 |
0.013 |
0.005 |
10.045 |
| Metro |
50.0 |
0.066 |
0.015 |
0.006 |
8.736 |
| DEMetro_Z |
2.1 |
0.044 |
0.015 |
0.006 |
5.132 |
| DEMetro_Z |
2.5 |
0.035 |
0.016 |
0.005 |
4.369 |
| DEMetro_Z |
3.0 |
0.032 |
0.015 |
0.006 |
3.114 |
| DEMetro_Z |
4.0 |
0.028 |
0.014 |
0.006 |
2.441 |
| DEMetro_Z |
10.0 |
0.029 |
0.013 |
0.005 |
3.246 |
| DEMetro_Z |
50.0 |
0.022 |
0.015 |
0.006 |
1.214 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Tails_with_high_Multimodality
(Mixture,
nu,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.453 |
2.54e-08 |
9.670 |
| HMC |
2.5 |
7.512 |
2.36e-08 |
11.991 |
| HMC |
3.0 |
6.325 |
6.31e-07 |
17.713 |
| HMC |
4.0 |
6.979 |
1.09e-07 |
21.149 |
| HMC |
10.0 |
9.059 |
5.77e-10 |
46.670 |
| HMC |
50.0 |
4.702 |
5.78e-05 |
23.689 |
| SMC |
2.1 |
5.992 |
1.44e-06 |
8.718 |
| SMC |
2.5 |
4.812 |
3.25e-05 |
3.554 |
| SMC |
3.0 |
5.410 |
5.22e-06 |
3.636 |
| SMC |
4.0 |
1.534 |
0.132 |
0.557 |
| SMC |
10.0 |
1.029 |
0.308 |
0.306 |
| SMC |
50.0 |
0.588 |
0.559 |
0.158 |
| Metro |
2.1 |
4.891 |
3.02e-05 |
5.443 |
| Metro |
2.5 |
4.700 |
4.05e-05 |
2.879 |
| Metro |
3.0 |
6.849 |
1.47e-07 |
14.298 |
| Metro |
4.0 |
7.114 |
7.63e-08 |
23.461 |
| Metro |
10.0 |
7.464 |
3.11e-08 |
35.842 |
| Metro |
50.0 |
5.692 |
3.68e-06 |
27.484 |
| DEMetro_Z |
2.1 |
6.899 |
1.31e-07 |
16.156 |
| DEMetro_Z |
2.5 |
5.843 |
2.39e-06 |
18.587 |
| DEMetro_Z |
3.0 |
6.004 |
1.55e-06 |
23.514 |
| DEMetro_Z |
4.0 |
8.102 |
5.91e-09 |
26.820 |
| DEMetro_Z |
10.0 |
7.136 |
7.31e-08 |
30.334 |
| DEMetro_Z |
50.0 |
7.998 |
7.8e-09 |
31.769 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.542
|
0.0166
|
-0.464
|
| HMC_vs_DEMetro_Z |
1
|
-1.725
|
0.0953
|
-0.315
|
| HMC_vs_DEMetro_Z |
2
|
-1.176
|
0.249
|
-0.215
|
| HMC_vs_DEMetro_Z |
3
|
-1.287
|
0.208
|
-0.235
|
| HMC_vs_DEMetro_Z |
4
|
2.368
|
0.0248
|
0.432
|
| HMC_vs_DEMetro_Z |
5
|
-1.591
|
0.122
|
-0.290
|
| Metro_vs_SMC |
0
|
-1.707
|
0.0984
|
-0.312
|
| Metro_vs_SMC |
1
|
-0.631
|
0.533
|
-0.115
|
| Metro_vs_SMC |
2
|
4.668
|
6.38e-05
|
0.852
|
| Metro_vs_SMC |
3
|
6.845
|
1.62e-07
|
1.250
|
| Metro_vs_SMC |
4
|
7.333
|
4.46e-08
|
1.339
|
| Metro_vs_SMC |
5
|
5.628
|
4.44e-06
|
1.028
|
| Metro_vs_DEMetro_Z |
0
|
-3.844
|
0.00061
|
-0.702
|
| Metro_vs_DEMetro_Z |
1
|
-5.018
|
2.41e-05
|
-0.916
|
| Metro_vs_DEMetro_Z |
2
|
-1.901
|
0.0672
|
-0.347
|
| Metro_vs_DEMetro_Z |
3
|
-0.633
|
0.532
|
-0.115
|
| Metro_vs_DEMetro_Z |
4
|
0.983
|
0.334
|
0.179
|
| Metro_vs_DEMetro_Z |
5
|
-0.793
|
0.434
|
-0.145
|
| HMC_vs_Metro |
0
|
2.630
|
0.0135
|
0.480
|
| HMC_vs_Metro |
1
|
5.550
|
5.51e-06
|
1.013
|
| HMC_vs_Metro |
2
|
0.945
|
0.353
|
0.173
|
| HMC_vs_Metro |
3
|
-0.565
|
0.576
|
-0.103
|
| HMC_vs_Metro |
4
|
1.728
|
0.0946
|
0.316
|
| HMC_vs_Metro |
5
|
-0.896
|
0.378
|
-0.164
|
| HMC_vs_SMC |
0
|
0.576
|
0.569
|
0.105
|
| HMC_vs_SMC |
1
|
4.894
|
3.4e-05
|
0.894
|
| HMC_vs_SMC |
2
|
5.099
|
1.92e-05
|
0.931
|
| HMC_vs_SMC |
3
|
6.693
|
2.43e-07
|
1.222
|
| HMC_vs_SMC |
4
|
9.014
|
6.59e-10
|
1.646
|
| HMC_vs_SMC |
5
|
4.618
|
7.33e-05
|
0.843
|
| DEMetro_Z_vs_SMC |
0
|
2.617
|
0.0139
|
0.478
|
| DEMetro_Z_vs_SMC |
1
|
4.517
|
9.69e-05
|
0.825
|
| DEMetro_Z_vs_SMC |
2
|
5.186
|
1.51e-05
|
0.947
|
| DEMetro_Z_vs_SMC |
3
|
8.080
|
6.54e-09
|
1.475
|
| DEMetro_Z_vs_SMC |
4
|
7.040
|
9.61e-08
|
1.285
|
| DEMetro_Z_vs_SMC |
5
|
7.888
|
1.06e-08
|
1.440
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.807 |
0.101 |
0.073 |
9.670 |
| HMC |
2.5 |
1.123 |
0.130 |
0.083 |
11.991 |
| HMC |
3.0 |
1.212 |
0.089 |
0.063 |
17.713 |
| HMC |
4.0 |
1.478 |
0.105 |
0.065 |
21.149 |
| HMC |
10.0 |
2.885 |
0.088 |
0.060 |
46.670 |
| HMC |
50.0 |
1.838 |
0.122 |
0.072 |
23.689 |
| SMC |
2.1 |
0.737 |
0.101 |
0.073 |
8.718 |
| SMC |
2.5 |
0.425 |
0.130 |
0.083 |
3.554 |
| SMC |
3.0 |
0.320 |
0.089 |
0.063 |
3.636 |
| SMC |
4.0 |
0.141 |
0.105 |
0.065 |
0.557 |
| SMC |
10.0 |
0.106 |
0.088 |
0.060 |
0.306 |
| SMC |
50.0 |
0.134 |
0.122 |
0.072 |
0.158 |
| Metro |
2.1 |
0.498 |
0.101 |
0.073 |
5.443 |
| Metro |
2.5 |
0.369 |
0.130 |
0.083 |
2.879 |
| Metro |
3.0 |
0.996 |
0.089 |
0.063 |
14.298 |
| Metro |
4.0 |
1.628 |
0.105 |
0.065 |
23.461 |
| Metro |
10.0 |
2.236 |
0.088 |
0.060 |
35.842 |
| Metro |
50.0 |
2.113 |
0.122 |
0.072 |
27.484 |
| DEMetro_Z |
2.1 |
1.280 |
0.101 |
0.073 |
16.156 |
| DEMetro_Z |
2.5 |
1.670 |
0.130 |
0.083 |
18.587 |
| DEMetro_Z |
3.0 |
1.580 |
0.089 |
0.063 |
23.514 |
| DEMetro_Z |
4.0 |
1.846 |
0.105 |
0.065 |
26.820 |
| DEMetro_Z |
10.0 |
1.906 |
0.088 |
0.060 |
30.334 |
| DEMetro_Z |
50.0 |
2.423 |
0.122 |
0.072 |
31.769 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.098 |
0.281 |
-0.205 |
| HMC |
2.5 |
1.552 |
0.127 |
0.496 |
| HMC |
3.0 |
3.908 |
0.000492 |
5.500 |
| HMC |
4.0 |
3.819 |
0.000651 |
22.897 |
| HMC |
10.0 |
5.749 |
3.18e-06 |
80.948 |
| HMC |
50.0 |
3.706 |
0.000884 |
76.016 |
| SMC |
2.1 |
-1.352 |
0.187 |
-0.248 |
| SMC |
2.5 |
0.102 |
0.919 |
0.023 |
| SMC |
3.0 |
1.021 |
0.313 |
0.437 |
| SMC |
4.0 |
0.487 |
0.628 |
0.136 |
| SMC |
10.0 |
-1.844 |
0.0709 |
-0.409 |
| SMC |
50.0 |
-0.244 |
0.808 |
-0.063 |
| Metro |
2.1 |
-1.317 |
0.198 |
-0.243 |
| Metro |
2.5 |
0.666 |
0.509 |
0.298 |
| Metro |
3.0 |
3.930 |
0.000447 |
4.147 |
| Metro |
4.0 |
3.965 |
0.000439 |
27.501 |
| Metro |
10.0 |
4.449 |
0.000117 |
54.516 |
| Metro |
50.0 |
4.267 |
0.000193 |
85.033 |
| DEMetro_Z |
2.1 |
-0.933 |
0.358 |
-0.173 |
| DEMetro_Z |
2.5 |
3.207 |
0.00295 |
2.184 |
| DEMetro_Z |
3.0 |
3.591 |
0.00119 |
11.678 |
| DEMetro_Z |
4.0 |
4.846 |
3.88e-05 |
33.218 |
| DEMetro_Z |
10.0 |
4.311 |
0.000171 |
39.643 |
| DEMetro_Z |
50.0 |
4.547 |
8.91e-05 |
86.212 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.090
|
0.285
|
0.199
|
| HMC_vs_SMC |
1
|
1.621
|
0.116
|
0.296
|
| HMC_vs_SMC |
2
|
3.740
|
0.000806
|
0.683
|
| HMC_vs_SMC |
3
|
3.825
|
0.000641
|
0.698
|
| HMC_vs_SMC |
4
|
5.793
|
2.82e-06
|
1.058
|
| HMC_vs_SMC |
5
|
3.716
|
0.00086
|
0.678
|
| Metro_vs_DEMetro_Z |
0
|
-2.665
|
0.0125
|
-0.487
|
| Metro_vs_DEMetro_Z |
1
|
-2.313
|
0.028
|
-0.422
|
| Metro_vs_DEMetro_Z |
2
|
-2.127
|
0.042
|
-0.388
|
| Metro_vs_DEMetro_Z |
3
|
-0.542
|
0.592
|
-0.099
|
| Metro_vs_DEMetro_Z |
4
|
1.047
|
0.304
|
0.191
|
| Metro_vs_DEMetro_Z |
5
|
-0.055
|
0.957
|
-0.010
|
| HMC_vs_Metro |
0
|
0.923
|
0.364
|
0.169
|
| HMC_vs_Metro |
1
|
0.418
|
0.679
|
0.076
|
| HMC_vs_Metro |
2
|
0.737
|
0.467
|
0.135
|
| HMC_vs_Metro |
3
|
-0.529
|
0.601
|
-0.097
|
| HMC_vs_Metro |
4
|
1.556
|
0.13
|
0.284
|
| HMC_vs_Metro |
5
|
-0.565
|
0.576
|
-0.103
|
| HMC_vs_DEMetro_Z |
0
|
-0.693
|
0.494
|
-0.126
|
| HMC_vs_DEMetro_Z |
1
|
-2.283
|
0.0299
|
-0.417
|
| HMC_vs_DEMetro_Z |
2
|
-1.673
|
0.105
|
-0.305
|
| HMC_vs_DEMetro_Z |
3
|
-1.168
|
0.252
|
-0.213
|
| HMC_vs_DEMetro_Z |
4
|
2.310
|
0.0282
|
0.422
|
| HMC_vs_DEMetro_Z |
5
|
-0.458
|
0.651
|
-0.084
|
| Metro_vs_SMC |
0
|
0.222
|
0.826
|
0.040
|
| Metro_vs_SMC |
1
|
0.623
|
0.538
|
0.114
|
| Metro_vs_SMC |
2
|
3.606
|
0.00115
|
0.658
|
| Metro_vs_SMC |
3
|
3.942
|
0.000469
|
0.720
|
| Metro_vs_SMC |
4
|
4.478
|
0.000108
|
0.817
|
| Metro_vs_SMC |
5
|
4.267
|
0.000193
|
0.779
|
| DEMetro_Z_vs_SMC |
0
|
2.400
|
0.023
|
0.438
|
| DEMetro_Z_vs_SMC |
1
|
3.464
|
0.00168
|
0.632
|
| DEMetro_Z_vs_SMC |
2
|
3.553
|
0.00133
|
0.649
|
| DEMetro_Z_vs_SMC |
3
|
4.841
|
3.95e-05
|
0.884
|
| DEMetro_Z_vs_SMC |
4
|
4.353
|
0.000152
|
0.795
|
| DEMetro_Z_vs_SMC |
5
|
4.559
|
8.63e-05
|
0.832
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
6.192 |
13.069 |
33.570 |
-0.205 |
| HMC |
2.5 |
3.497 |
2.307 |
2.397 |
0.496 |
| HMC |
3.0 |
3.654 |
0.685 |
0.540 |
5.500 |
| HMC |
4.0 |
4.752 |
0.338 |
0.193 |
22.897 |
| HMC |
10.0 |
15.878 |
0.247 |
0.193 |
80.948 |
| HMC |
50.0 |
10.233 |
0.220 |
0.132 |
76.016 |
| SMC |
2.1 |
4.744 |
13.069 |
33.570 |
-0.248 |
| SMC |
2.5 |
2.363 |
2.307 |
2.397 |
0.023 |
| SMC |
3.0 |
0.920 |
0.685 |
0.540 |
0.437 |
| SMC |
4.0 |
0.365 |
0.338 |
0.193 |
0.136 |
| SMC |
10.0 |
0.168 |
0.247 |
0.193 |
-0.409 |
| SMC |
50.0 |
0.211 |
0.220 |
0.132 |
-0.063 |
| Metro |
2.1 |
4.920 |
13.069 |
33.570 |
-0.243 |
| Metro |
2.5 |
3.021 |
2.307 |
2.397 |
0.298 |
| Metro |
3.0 |
2.924 |
0.685 |
0.540 |
4.147 |
| Metro |
4.0 |
5.640 |
0.338 |
0.193 |
27.501 |
| Metro |
10.0 |
10.774 |
0.247 |
0.193 |
54.516 |
| Metro |
50.0 |
11.420 |
0.220 |
0.132 |
85.033 |
| DEMetro_Z |
2.1 |
7.275 |
13.069 |
33.570 |
-0.173 |
| DEMetro_Z |
2.5 |
7.543 |
2.307 |
2.397 |
2.184 |
| DEMetro_Z |
3.0 |
6.991 |
0.685 |
0.540 |
11.678 |
| DEMetro_Z |
4.0 |
6.742 |
0.338 |
0.193 |
33.218 |
| DEMetro_Z |
10.0 |
7.902 |
0.247 |
0.193 |
39.643 |
| DEMetro_Z |
50.0 |
11.576 |
0.220 |
0.132 |
86.212 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.522 |
1.95e-08 |
8.471 |
| HMC |
2.5 |
7.587 |
1.95e-08 |
12.265 |
| HMC |
3.0 |
6.536 |
3.59e-07 |
20.442 |
| HMC |
4.0 |
6.829 |
1.64e-07 |
24.047 |
| HMC |
10.0 |
9.137 |
4.81e-10 |
50.455 |
| HMC |
50.0 |
4.674 |
6.23e-05 |
23.891 |
| SMC |
2.1 |
8.060 |
4.69e-09 |
9.116 |
| SMC |
2.5 |
6.647 |
1.4e-07 |
4.620 |
| SMC |
3.0 |
5.962 |
1.14e-06 |
4.562 |
| SMC |
4.0 |
1.900 |
0.0641 |
0.751 |
| SMC |
10.0 |
1.056 |
0.296 |
0.316 |
| SMC |
50.0 |
0.466 |
0.643 |
0.123 |
| Metro |
2.1 |
5.380 |
7.11e-06 |
5.159 |
| Metro |
2.5 |
5.758 |
1.61e-06 |
3.413 |
| Metro |
3.0 |
6.941 |
1.18e-07 |
17.512 |
| Metro |
4.0 |
7.555 |
2.42e-08 |
26.307 |
| Metro |
10.0 |
7.361 |
4.08e-08 |
38.789 |
| Metro |
50.0 |
5.714 |
3.46e-06 |
28.491 |
| DEMetro_Z |
2.1 |
7.537 |
2.34e-08 |
14.719 |
| DEMetro_Z |
2.5 |
6.184 |
9.34e-07 |
18.810 |
| DEMetro_Z |
3.0 |
6.067 |
1.31e-06 |
28.851 |
| DEMetro_Z |
4.0 |
7.796 |
1.31e-08 |
30.911 |
| DEMetro_Z |
10.0 |
7.309 |
4.64e-08 |
32.869 |
| DEMetro_Z |
50.0 |
7.847 |
1.15e-08 |
32.898 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-4.237
|
0.00021
|
-0.773
|
| Metro_vs_DEMetro_Z |
1
|
-5.058
|
2.16e-05
|
-0.924
|
| Metro_vs_DEMetro_Z |
2
|
-1.955
|
0.0602
|
-0.357
|
| Metro_vs_DEMetro_Z |
3
|
-0.761
|
0.453
|
-0.139
|
| Metro_vs_DEMetro_Z |
4
|
0.983
|
0.334
|
0.179
|
| Metro_vs_DEMetro_Z |
5
|
-0.767
|
0.449
|
-0.140
|
| DEMetro_Z_vs_SMC |
0
|
2.352
|
0.0257
|
0.429
|
| DEMetro_Z_vs_SMC |
1
|
4.628
|
7.13e-05
|
0.845
|
| DEMetro_Z_vs_SMC |
2
|
5.211
|
1.41e-05
|
0.951
|
| DEMetro_Z_vs_SMC |
3
|
7.754
|
1.5e-08
|
1.416
|
| DEMetro_Z_vs_SMC |
4
|
7.208
|
6.18e-08
|
1.316
|
| DEMetro_Z_vs_SMC |
5
|
7.774
|
1.42e-08
|
1.419
|
| HMC_vs_DEMetro_Z |
0
|
-2.912
|
0.00684
|
-0.532
|
| HMC_vs_DEMetro_Z |
1
|
-1.763
|
0.0884
|
-0.322
|
| HMC_vs_DEMetro_Z |
2
|
-1.451
|
0.158
|
-0.265
|
| HMC_vs_DEMetro_Z |
3
|
-1.311
|
0.2
|
-0.239
|
| HMC_vs_DEMetro_Z |
4
|
2.436
|
0.0212
|
0.445
|
| HMC_vs_DEMetro_Z |
5
|
-1.698
|
0.1
|
-0.310
|
| HMC_vs_Metro |
0
|
2.584
|
0.0151
|
0.472
|
| HMC_vs_Metro |
1
|
5.330
|
1.01e-05
|
0.973
|
| HMC_vs_Metro |
2
|
0.711
|
0.483
|
0.130
|
| HMC_vs_Metro |
3
|
-0.506
|
0.617
|
-0.092
|
| HMC_vs_Metro |
4
|
1.686
|
0.102
|
0.308
|
| HMC_vs_Metro |
5
|
-1.054
|
0.3
|
-0.192
|
| HMC_vs_SMC |
0
|
-0.493
|
0.626
|
-0.090
|
| HMC_vs_SMC |
1
|
4.459
|
0.000114
|
0.814
|
| HMC_vs_SMC |
2
|
5.173
|
1.57e-05
|
0.945
|
| HMC_vs_SMC |
3
|
6.544
|
3.63e-07
|
1.195
|
| HMC_vs_SMC |
4
|
9.115
|
5.17e-10
|
1.664
|
| HMC_vs_SMC |
5
|
4.606
|
7.57e-05
|
0.841
|
| Metro_vs_SMC |
0
|
-2.499
|
0.0184
|
-0.456
|
| Metro_vs_SMC |
1
|
-1.188
|
0.245
|
-0.217
|
| Metro_vs_SMC |
2
|
4.761
|
4.93e-05
|
0.869
|
| Metro_vs_SMC |
3
|
7.160
|
7e-08
|
1.307
|
| Metro_vs_SMC |
4
|
7.241
|
5.67e-08
|
1.322
|
| Metro_vs_SMC |
5
|
5.670
|
3.95e-06
|
1.035
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.814 |
0.179 |
0.075 |
8.471 |
| HMC |
2.5 |
1.077 |
0.180 |
0.073 |
12.265 |
| HMC |
3.0 |
1.085 |
0.123 |
0.047 |
20.442 |
| HMC |
4.0 |
1.345 |
0.127 |
0.051 |
24.047 |
| HMC |
10.0 |
2.598 |
0.101 |
0.049 |
50.455 |
| HMC |
50.0 |
1.624 |
0.126 |
0.063 |
23.891 |
| SMC |
2.1 |
0.862 |
0.179 |
0.075 |
9.116 |
| SMC |
2.5 |
0.518 |
0.180 |
0.073 |
4.620 |
| SMC |
3.0 |
0.338 |
0.123 |
0.047 |
4.562 |
| SMC |
4.0 |
0.165 |
0.127 |
0.051 |
0.751 |
| SMC |
10.0 |
0.117 |
0.101 |
0.049 |
0.316 |
| SMC |
50.0 |
0.134 |
0.126 |
0.063 |
0.123 |
| Metro |
2.1 |
0.566 |
0.179 |
0.075 |
5.159 |
| Metro |
2.5 |
0.429 |
0.180 |
0.073 |
3.413 |
| Metro |
3.0 |
0.947 |
0.123 |
0.047 |
17.512 |
| Metro |
4.0 |
1.460 |
0.127 |
0.051 |
26.307 |
| Metro |
10.0 |
2.021 |
0.101 |
0.049 |
38.789 |
| Metro |
50.0 |
1.912 |
0.126 |
0.063 |
28.491 |
| DEMetro_Z |
2.1 |
1.282 |
0.179 |
0.075 |
14.719 |
| DEMetro_Z |
2.5 |
1.556 |
0.180 |
0.073 |
18.810 |
| DEMetro_Z |
3.0 |
1.480 |
0.123 |
0.047 |
28.851 |
| DEMetro_Z |
4.0 |
1.693 |
0.127 |
0.051 |
30.911 |
| DEMetro_Z |
10.0 |
1.728 |
0.101 |
0.049 |
32.869 |
| DEMetro_Z |
50.0 |
2.188 |
0.126 |
0.063 |
32.898 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.112 |
6.94e-08 |
11.868 |
| HMC |
2.5 |
7.178 |
6.04e-08 |
14.065 |
| HMC |
3.0 |
6.103 |
1.17e-06 |
21.609 |
| HMC |
4.0 |
6.857 |
1.52e-07 |
24.973 |
| HMC |
10.0 |
9.378 |
2.72e-10 |
54.882 |
| HMC |
50.0 |
4.833 |
4.01e-05 |
27.274 |
| SMC |
2.1 |
6.012 |
1.43e-06 |
11.190 |
| SMC |
2.5 |
5.179 |
1.15e-05 |
4.051 |
| SMC |
3.0 |
5.395 |
5.93e-06 |
4.041 |
| SMC |
4.0 |
1.618 |
0.113 |
0.595 |
| SMC |
10.0 |
1.155 |
0.253 |
0.341 |
| SMC |
50.0 |
0.317 |
0.753 |
0.089 |
| Metro |
2.1 |
4.878 |
3.27e-05 |
6.615 |
| Metro |
2.5 |
4.425 |
9.7e-05 |
3.022 |
| Metro |
3.0 |
6.450 |
4.47e-07 |
17.326 |
| Metro |
4.0 |
7.147 |
7.07e-08 |
27.590 |
| Metro |
10.0 |
7.851 |
1.15e-08 |
42.274 |
| Metro |
50.0 |
5.852 |
2.37e-06 |
31.546 |
| DEMetro_Z |
2.1 |
6.845 |
1.56e-07 |
21.596 |
| DEMetro_Z |
2.5 |
5.683 |
3.76e-06 |
22.344 |
| DEMetro_Z |
3.0 |
5.755 |
3.1e-06 |
29.514 |
| DEMetro_Z |
4.0 |
8.078 |
6.37e-09 |
31.328 |
| DEMetro_Z |
10.0 |
7.351 |
4.18e-08 |
36.440 |
| DEMetro_Z |
50.0 |
8.531 |
2.07e-09 |
36.860 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
2.725
|
0.0108
|
0.497
|
| DEMetro_Z_vs_SMC |
1
|
4.508
|
9.93e-05
|
0.823
|
| DEMetro_Z_vs_SMC |
2
|
5.084
|
2.01e-05
|
0.928
|
| DEMetro_Z_vs_SMC |
3
|
8.032
|
7.39e-09
|
1.466
|
| DEMetro_Z_vs_SMC |
4
|
7.280
|
5.12e-08
|
1.329
|
| DEMetro_Z_vs_SMC |
5
|
8.442
|
2.66e-09
|
1.541
|
| HMC_vs_Metro |
0
|
2.648
|
0.013
|
0.483
|
| HMC_vs_Metro |
1
|
5.617
|
4.58e-06
|
1.025
|
| HMC_vs_Metro |
2
|
0.935
|
0.358
|
0.171
|
| HMC_vs_Metro |
3
|
-0.539
|
0.594
|
-0.098
|
| HMC_vs_Metro |
4
|
1.820
|
0.079
|
0.332
|
| HMC_vs_Metro |
5
|
-0.905
|
0.373
|
-0.165
|
| Metro_vs_DEMetro_Z |
0
|
-4.085
|
0.000317
|
-0.746
|
| Metro_vs_DEMetro_Z |
1
|
-5.014
|
2.44e-05
|
-0.915
|
| Metro_vs_DEMetro_Z |
2
|
-1.945
|
0.0615
|
-0.355
|
| Metro_vs_DEMetro_Z |
3
|
-0.599
|
0.554
|
-0.109
|
| Metro_vs_DEMetro_Z |
4
|
0.924
|
0.363
|
0.169
|
| Metro_vs_DEMetro_Z |
5
|
-0.873
|
0.39
|
-0.159
|
| HMC_vs_SMC |
0
|
0.327
|
0.746
|
0.060
|
| HMC_vs_SMC |
1
|
4.899
|
3.36e-05
|
0.894
|
| HMC_vs_SMC |
2
|
5.043
|
2.25e-05
|
0.921
|
| HMC_vs_SMC |
3
|
6.646
|
2.75e-07
|
1.213
|
| HMC_vs_SMC |
4
|
9.328
|
3.12e-10
|
1.703
|
| HMC_vs_SMC |
5
|
4.765
|
4.88e-05
|
0.870
|
| Metro_vs_SMC |
0
|
-1.861
|
0.0729
|
-0.340
|
| Metro_vs_SMC |
1
|
-0.910
|
0.371
|
-0.166
|
| Metro_vs_SMC |
2
|
4.525
|
9.47e-05
|
0.826
|
| Metro_vs_SMC |
3
|
6.893
|
1.42e-07
|
1.259
|
| Metro_vs_SMC |
4
|
7.727
|
1.61e-08
|
1.411
|
| Metro_vs_SMC |
5
|
5.807
|
2.71e-06
|
1.060
|
| HMC_vs_DEMetro_Z |
0
|
-2.793
|
0.00915
|
-0.510
|
| HMC_vs_DEMetro_Z |
1
|
-1.747
|
0.0912
|
-0.319
|
| HMC_vs_DEMetro_Z |
2
|
-1.233
|
0.228
|
-0.225
|
| HMC_vs_DEMetro_Z |
3
|
-1.226
|
0.23
|
-0.224
|
| HMC_vs_DEMetro_Z |
4
|
2.345
|
0.0261
|
0.428
|
| HMC_vs_DEMetro_Z |
5
|
-1.667
|
0.106
|
-0.304
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.081 |
0.010 |
0.006 |
11.868 |
| HMC |
2.5 |
0.121 |
0.014 |
0.008 |
14.065 |
| HMC |
3.0 |
0.134 |
0.010 |
0.006 |
21.609 |
| HMC |
4.0 |
0.171 |
0.012 |
0.006 |
24.973 |
| HMC |
10.0 |
0.327 |
0.010 |
0.006 |
54.882 |
| HMC |
50.0 |
0.207 |
0.013 |
0.007 |
27.274 |
| SMC |
2.1 |
0.077 |
0.010 |
0.006 |
11.190 |
| SMC |
2.5 |
0.044 |
0.014 |
0.008 |
4.051 |
| SMC |
3.0 |
0.033 |
0.010 |
0.006 |
4.041 |
| SMC |
4.0 |
0.015 |
0.012 |
0.006 |
0.595 |
| SMC |
10.0 |
0.012 |
0.010 |
0.006 |
0.341 |
| SMC |
50.0 |
0.014 |
0.013 |
0.007 |
0.089 |
| Metro |
2.1 |
0.049 |
0.010 |
0.006 |
6.615 |
| Metro |
2.5 |
0.037 |
0.014 |
0.008 |
3.022 |
| Metro |
3.0 |
0.110 |
0.010 |
0.006 |
17.326 |
| Metro |
4.0 |
0.187 |
0.012 |
0.006 |
27.590 |
| Metro |
10.0 |
0.254 |
0.010 |
0.006 |
42.274 |
| Metro |
50.0 |
0.237 |
0.013 |
0.007 |
31.546 |
| DEMetro_Z |
2.1 |
0.138 |
0.010 |
0.006 |
21.596 |
| DEMetro_Z |
2.5 |
0.184 |
0.014 |
0.008 |
22.344 |
| DEMetro_Z |
3.0 |
0.180 |
0.010 |
0.006 |
29.514 |
| DEMetro_Z |
4.0 |
0.211 |
0.012 |
0.006 |
31.328 |
| DEMetro_Z |
10.0 |
0.220 |
0.010 |
0.006 |
36.440 |
| DEMetro_Z |
50.0 |
0.275 |
0.013 |
0.007 |
36.860 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.196 |
5.61e-08 |
12.623 |
| HMC |
2.5 |
6.070 |
1.15e-06 |
8.593 |
| HMC |
3.0 |
6.692 |
2.37e-07 |
23.373 |
| HMC |
4.0 |
5.970 |
1.71e-06 |
30.188 |
| HMC |
10.0 |
41.725 |
9.92e-28 |
90.597 |
| HMC |
50.0 |
263.274 |
6.09e-88 |
76.091 |
| SMC |
2.1 |
5.683 |
3.4e-06 |
8.122 |
| SMC |
2.5 |
3.844 |
0.000562 |
3.799 |
| SMC |
3.0 |
3.179 |
0.00283 |
1.399 |
| SMC |
4.0 |
1.816 |
0.0748 |
0.521 |
| SMC |
10.0 |
0.036 |
0.972 |
0.009 |
| SMC |
50.0 |
-1.957 |
0.0554 |
-0.462 |
| Metro |
2.1 |
3.289 |
0.00258 |
4.967 |
| Metro |
2.5 |
5.533 |
2.71e-06 |
2.890 |
| Metro |
3.0 |
4.967 |
2.65e-05 |
9.176 |
| Metro |
4.0 |
5.409 |
8.07e-06 |
26.648 |
| Metro |
10.0 |
16.285 |
3.75e-16 |
82.290 |
| Metro |
50.0 |
249.087 |
1.14e-83 |
76.330 |
| DEMetro_Z |
2.1 |
4.919 |
3.1e-05 |
12.710 |
| DEMetro_Z |
2.5 |
4.716 |
5.49e-05 |
14.451 |
| DEMetro_Z |
3.0 |
4.250 |
0.000202 |
21.843 |
| DEMetro_Z |
4.0 |
6.604 |
3.06e-07 |
43.616 |
| DEMetro_Z |
10.0 |
9.039 |
6.13e-10 |
64.401 |
| DEMetro_Z |
50.0 |
13.205 |
8.18e-14 |
64.135 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.028
|
0.978
|
-0.005
|
| HMC_vs_DEMetro_Z |
1
|
-1.556
|
0.13
|
-0.284
|
| HMC_vs_DEMetro_Z |
2
|
0.243
|
0.809
|
0.044
|
| HMC_vs_DEMetro_Z |
3
|
-1.791
|
0.0837
|
-0.327
|
| HMC_vs_DEMetro_Z |
4
|
3.883
|
0.000549
|
0.709
|
| HMC_vs_DEMetro_Z |
5
|
2.469
|
0.0197
|
0.451
|
| Metro_vs_SMC |
0
|
-1.654
|
0.109
|
-0.302
|
| Metro_vs_SMC |
1
|
-0.826
|
0.415
|
-0.151
|
| Metro_vs_SMC |
2
|
4.181
|
0.000244
|
0.763
|
| Metro_vs_SMC |
3
|
5.245
|
1.28e-05
|
0.958
|
| Metro_vs_SMC |
4
|
16.199
|
4.55e-16
|
2.957
|
| Metro_vs_SMC |
5
|
256.354
|
3.26e-50
|
46.804
|
| Metro_vs_DEMetro_Z |
0
|
-2.585
|
0.015
|
-0.472
|
| Metro_vs_DEMetro_Z |
1
|
-3.768
|
0.000748
|
-0.688
|
| Metro_vs_DEMetro_Z |
2
|
-2.372
|
0.0245
|
-0.433
|
| Metro_vs_DEMetro_Z |
3
|
-2.270
|
0.0308
|
-0.414
|
| Metro_vs_DEMetro_Z |
4
|
1.851
|
0.0744
|
0.338
|
| Metro_vs_DEMetro_Z |
5
|
2.493
|
0.0186
|
0.455
|
| HMC_vs_Metro |
0
|
3.092
|
0.00437
|
0.564
|
| HMC_vs_Metro |
1
|
3.871
|
0.000568
|
0.707
|
| HMC_vs_Metro |
2
|
4.030
|
0.000369
|
0.736
|
| HMC_vs_Metro |
3
|
0.562
|
0.579
|
0.103
|
| HMC_vs_Metro |
4
|
1.468
|
0.153
|
0.268
|
| HMC_vs_Metro |
5
|
-1.451
|
0.158
|
-0.265
|
| HMC_vs_SMC |
0
|
2.270
|
0.0308
|
0.414
|
| HMC_vs_SMC |
1
|
2.766
|
0.00976
|
0.505
|
| HMC_vs_SMC |
2
|
6.252
|
8.01e-07
|
1.141
|
| HMC_vs_SMC |
3
|
5.784
|
2.88e-06
|
1.056
|
| HMC_vs_SMC |
4
|
41.131
|
2.87e-27
|
7.509
|
| HMC_vs_SMC |
5
|
273.886
|
4.79e-51
|
50.004
|
| DEMetro_Z_vs_SMC |
0
|
1.385
|
0.177
|
0.253
|
| DEMetro_Z_vs_SMC |
1
|
3.272
|
0.00276
|
0.597
|
| DEMetro_Z_vs_SMC |
2
|
3.931
|
0.000482
|
0.718
|
| DEMetro_Z_vs_SMC |
3
|
6.553
|
3.53e-07
|
1.196
|
| DEMetro_Z_vs_SMC |
4
|
9.047
|
6.09e-10
|
1.652
|
| DEMetro_Z_vs_SMC |
5
|
13.342
|
6.61e-14
|
2.436
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
1.022 |
0.101 |
0.073 |
12.623 |
| HMC |
2.5 |
0.842 |
0.130 |
0.083 |
8.593 |
| HMC |
3.0 |
1.571 |
0.089 |
0.063 |
23.373 |
| HMC |
4.0 |
2.065 |
0.105 |
0.065 |
30.188 |
| HMC |
10.0 |
5.518 |
0.088 |
0.060 |
90.597 |
| HMC |
50.0 |
5.632 |
0.122 |
0.072 |
76.091 |
| SMC |
2.1 |
0.694 |
0.101 |
0.073 |
8.122 |
| SMC |
2.5 |
0.445 |
0.130 |
0.083 |
3.799 |
| SMC |
3.0 |
0.178 |
0.089 |
0.063 |
1.399 |
| SMC |
4.0 |
0.139 |
0.105 |
0.065 |
0.521 |
| SMC |
10.0 |
0.088 |
0.088 |
0.060 |
0.009 |
| SMC |
50.0 |
0.089 |
0.122 |
0.072 |
-0.462 |
| Metro |
2.1 |
0.463 |
0.101 |
0.073 |
4.967 |
| Metro |
2.5 |
0.370 |
0.130 |
0.083 |
2.890 |
| Metro |
3.0 |
0.671 |
0.089 |
0.063 |
9.176 |
| Metro |
4.0 |
1.835 |
0.105 |
0.065 |
26.648 |
| Metro |
10.0 |
5.020 |
0.088 |
0.060 |
82.290 |
| Metro |
50.0 |
5.650 |
0.122 |
0.072 |
76.330 |
| DEMetro_Z |
2.1 |
1.028 |
0.101 |
0.073 |
12.710 |
| DEMetro_Z |
2.5 |
1.327 |
0.130 |
0.083 |
14.451 |
| DEMetro_Z |
3.0 |
1.474 |
0.089 |
0.063 |
21.843 |
| DEMetro_Z |
4.0 |
2.936 |
0.105 |
0.065 |
43.616 |
| DEMetro_Z |
10.0 |
3.948 |
0.088 |
0.060 |
64.401 |
| DEMetro_Z |
50.0 |
4.767 |
0.122 |
0.072 |
64.135 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.087 |
0.285 |
-0.204 |
| HMC |
2.5 |
0.272 |
0.787 |
0.063 |
| HMC |
3.0 |
3.796 |
0.000686 |
9.488 |
| HMC |
4.0 |
4.039 |
0.00036 |
53.527 |
| HMC |
10.0 |
31.721 |
4.34e-24 |
225.838 |
| HMC |
50.0 |
1185.645 |
1.2e-124 |
341.184 |
| SMC |
2.1 |
-1.628 |
0.114 |
-0.298 |
| SMC |
2.5 |
-0.596 |
0.554 |
-0.144 |
| SMC |
3.0 |
0.108 |
0.914 |
0.043 |
| SMC |
4.0 |
0.918 |
0.362 |
0.254 |
| SMC |
10.0 |
-0.101 |
0.92 |
-0.024 |
| SMC |
50.0 |
-0.018 |
0.986 |
-0.005 |
| Metro |
2.1 |
-1.110 |
0.276 |
-0.206 |
| Metro |
2.5 |
0.620 |
0.539 |
0.317 |
| Metro |
3.0 |
2.582 |
0.0147 |
2.422 |
| Metro |
4.0 |
3.767 |
0.00075 |
45.910 |
| Metro |
10.0 |
14.260 |
1.22e-14 |
202.850 |
| Metro |
50.0 |
1165.230 |
5.4e-123 |
341.298 |
| DEMetro_Z |
2.1 |
-1.034 |
0.309 |
-0.193 |
| DEMetro_Z |
2.5 |
2.423 |
0.0211 |
1.814 |
| DEMetro_Z |
3.0 |
2.739 |
0.0104 |
13.994 |
| DEMetro_Z |
4.0 |
5.378 |
8.88e-06 |
103.706 |
| DEMetro_Z |
10.0 |
7.708 |
1.68e-08 |
150.997 |
| DEMetro_Z |
50.0 |
11.878 |
1.16e-12 |
279.115 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.628
|
0.0136
|
0.480
|
| HMC_vs_SMC |
1
|
1.015
|
0.318
|
0.185
|
| HMC_vs_SMC |
2
|
3.755
|
0.000775
|
0.686
|
| HMC_vs_SMC |
3
|
4.004
|
0.000396
|
0.731
|
| HMC_vs_SMC |
4
|
31.677
|
4.75e-24
|
5.783
|
| HMC_vs_SMC |
5
|
1168.236
|
2.59e-69
|
213.290
|
| Metro_vs_DEMetro_Z |
0
|
-0.268
|
0.79
|
-0.049
|
| Metro_vs_DEMetro_Z |
1
|
-1.647
|
0.11
|
-0.301
|
| Metro_vs_DEMetro_Z |
2
|
-2.275
|
0.0305
|
-0.415
|
| Metro_vs_DEMetro_Z |
3
|
-2.959
|
0.0061
|
-0.540
|
| Metro_vs_DEMetro_Z |
4
|
1.947
|
0.0613
|
0.355
|
| Metro_vs_DEMetro_Z |
5
|
2.643
|
0.0131
|
0.483
|
| HMC_vs_Metro |
0
|
0.033
|
0.974
|
0.006
|
| HMC_vs_Metro |
1
|
-0.488
|
0.629
|
-0.089
|
| HMC_vs_Metro |
2
|
2.828
|
0.00841
|
0.516
|
| HMC_vs_Metro |
3
|
0.451
|
0.655
|
0.082
|
| HMC_vs_Metro |
4
|
1.400
|
0.172
|
0.256
|
| HMC_vs_Metro |
5
|
-1.864
|
0.0725
|
-0.340
|
| HMC_vs_DEMetro_Z |
0
|
-0.199
|
0.843
|
-0.036
|
| HMC_vs_DEMetro_Z |
1
|
-2.306
|
0.0285
|
-0.421
|
| HMC_vs_DEMetro_Z |
2
|
-0.800
|
0.43
|
-0.146
|
| HMC_vs_DEMetro_Z |
3
|
-2.324
|
0.0273
|
-0.424
|
| HMC_vs_DEMetro_Z |
4
|
3.947
|
0.000462
|
0.721
|
| HMC_vs_DEMetro_Z |
5
|
2.639
|
0.0132
|
0.482
|
| Metro_vs_SMC |
0
|
3.245
|
0.00296
|
0.592
|
| Metro_vs_SMC |
1
|
0.940
|
0.355
|
0.172
|
| Metro_vs_SMC |
2
|
2.739
|
0.0104
|
0.500
|
| Metro_vs_SMC |
3
|
3.739
|
0.000808
|
0.683
|
| Metro_vs_SMC |
4
|
14.299
|
1.15e-14
|
2.611
|
| Metro_vs_SMC |
5
|
1119.483
|
8.92e-69
|
204.389
|
| DEMetro_Z_vs_SMC |
0
|
2.889
|
0.00724
|
0.527
|
| DEMetro_Z_vs_SMC |
1
|
2.628
|
0.0136
|
0.480
|
| DEMetro_Z_vs_SMC |
2
|
2.815
|
0.00867
|
0.514
|
| DEMetro_Z_vs_SMC |
3
|
5.350
|
9.59e-06
|
0.977
|
| DEMetro_Z_vs_SMC |
4
|
7.694
|
1.75e-08
|
1.405
|
| DEMetro_Z_vs_SMC |
5
|
11.880
|
1.16e-12
|
2.169
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
6.222 |
13.069 |
33.570 |
-0.204 |
| HMC |
2.5 |
2.459 |
2.307 |
2.397 |
0.063 |
| HMC |
3.0 |
5.808 |
0.685 |
0.540 |
9.488 |
| HMC |
4.0 |
10.657 |
0.338 |
0.193 |
53.527 |
| HMC |
10.0 |
43.857 |
0.247 |
0.193 |
225.838 |
| HMC |
50.0 |
45.161 |
0.220 |
0.132 |
341.184 |
| SMC |
2.1 |
3.060 |
13.069 |
33.570 |
-0.298 |
| SMC |
2.5 |
1.962 |
2.307 |
2.397 |
-0.144 |
| SMC |
3.0 |
0.708 |
0.685 |
0.540 |
0.043 |
| SMC |
4.0 |
0.387 |
0.338 |
0.193 |
0.254 |
| SMC |
10.0 |
0.242 |
0.247 |
0.193 |
-0.024 |
| SMC |
50.0 |
0.219 |
0.220 |
0.132 |
-0.005 |
| Metro |
2.1 |
6.168 |
13.069 |
33.570 |
-0.206 |
| Metro |
2.5 |
3.065 |
2.307 |
2.397 |
0.317 |
| Metro |
3.0 |
1.992 |
0.685 |
0.540 |
2.422 |
| Metro |
4.0 |
9.189 |
0.338 |
0.193 |
45.910 |
| Metro |
10.0 |
39.418 |
0.247 |
0.193 |
202.850 |
| Metro |
50.0 |
45.176 |
0.220 |
0.132 |
341.298 |
| DEMetro_Z |
2.1 |
6.584 |
13.069 |
33.570 |
-0.193 |
| DEMetro_Z |
2.5 |
6.654 |
2.307 |
2.397 |
1.814 |
| DEMetro_Z |
3.0 |
8.241 |
0.685 |
0.540 |
13.994 |
| DEMetro_Z |
4.0 |
20.331 |
0.338 |
0.193 |
103.706 |
| DEMetro_Z |
10.0 |
29.405 |
0.247 |
0.193 |
150.997 |
| DEMetro_Z |
50.0 |
36.985 |
0.220 |
0.132 |
279.115 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.104 |
6.96e-08 |
11.177 |
| HMC |
2.5 |
5.883 |
1.95e-06 |
8.505 |
| HMC |
3.0 |
6.837 |
1.62e-07 |
28.030 |
| HMC |
4.0 |
5.747 |
3.17e-06 |
34.282 |
| HMC |
10.0 |
36.294 |
6.96e-26 |
99.713 |
| HMC |
50.0 |
75.688 |
1.47e-36 |
79.582 |
| SMC |
2.1 |
6.388 |
4.43e-07 |
7.442 |
| SMC |
2.5 |
3.986 |
0.000387 |
4.421 |
| SMC |
3.0 |
3.702 |
0.000689 |
1.892 |
| SMC |
4.0 |
2.024 |
0.0479 |
0.596 |
| SMC |
10.0 |
0.032 |
0.974 |
0.008 |
| SMC |
50.0 |
-1.746 |
0.0866 |
-0.398 |
| Metro |
2.1 |
3.712 |
0.000833 |
4.898 |
| Metro |
2.5 |
6.707 |
6.81e-08 |
3.447 |
| Metro |
3.0 |
5.173 |
1.51e-05 |
11.727 |
| Metro |
4.0 |
5.331 |
1e-05 |
30.916 |
| Metro |
10.0 |
15.993 |
6.08e-16 |
89.147 |
| Metro |
50.0 |
76.419 |
9.82e-37 |
79.260 |
| DEMetro_Z |
2.1 |
5.170 |
1.53e-05 |
12.051 |
| DEMetro_Z |
2.5 |
4.988 |
2.57e-05 |
15.094 |
| DEMetro_Z |
3.0 |
4.407 |
0.000131 |
27.289 |
| DEMetro_Z |
4.0 |
6.667 |
2.59e-07 |
50.254 |
| DEMetro_Z |
10.0 |
8.983 |
7.02e-10 |
69.183 |
| DEMetro_Z |
50.0 |
13.122 |
9.6e-14 |
65.426 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.660
|
0.0126
|
-0.486
|
| Metro_vs_DEMetro_Z |
1
|
-3.806
|
0.000676
|
-0.695
|
| Metro_vs_DEMetro_Z |
2
|
-2.389
|
0.0236
|
-0.436
|
| Metro_vs_DEMetro_Z |
3
|
-2.304
|
0.0286
|
-0.421
|
| Metro_vs_DEMetro_Z |
4
|
1.872
|
0.0713
|
0.342
|
| Metro_vs_DEMetro_Z |
5
|
2.784
|
0.00936
|
0.508
|
| DEMetro_Z_vs_SMC |
0
|
1.591
|
0.122
|
0.291
|
| DEMetro_Z_vs_SMC |
1
|
3.298
|
0.00258
|
0.602
|
| DEMetro_Z_vs_SMC |
2
|
4.083
|
0.000319
|
0.745
|
| DEMetro_Z_vs_SMC |
3
|
6.606
|
3.06e-07
|
1.206
|
| DEMetro_Z_vs_SMC |
4
|
9.010
|
6.65e-10
|
1.645
|
| DEMetro_Z_vs_SMC |
5
|
13.268
|
7.6e-14
|
2.422
|
| HMC_vs_DEMetro_Z |
0
|
-0.305
|
0.763
|
-0.056
|
| HMC_vs_DEMetro_Z |
1
|
-1.753
|
0.0901
|
-0.320
|
| HMC_vs_DEMetro_Z |
2
|
0.098
|
0.922
|
0.018
|
| HMC_vs_DEMetro_Z |
3
|
-1.873
|
0.0712
|
-0.342
|
| HMC_vs_DEMetro_Z |
4
|
3.885
|
0.000547
|
0.709
|
| HMC_vs_DEMetro_Z |
5
|
2.883
|
0.00735
|
0.526
|
| HMC_vs_Metro |
0
|
2.854
|
0.00789
|
0.521
|
| HMC_vs_Metro |
1
|
3.380
|
0.00209
|
0.617
|
| HMC_vs_Metro |
2
|
3.986
|
0.000415
|
0.728
|
| HMC_vs_Metro |
3
|
0.452
|
0.654
|
0.083
|
| HMC_vs_Metro |
4
|
1.700
|
0.0999
|
0.310
|
| HMC_vs_Metro |
5
|
0.220
|
0.827
|
0.040
|
| HMC_vs_SMC |
0
|
2.173
|
0.0381
|
0.397
|
| HMC_vs_SMC |
1
|
2.211
|
0.0351
|
0.404
|
| HMC_vs_SMC |
2
|
6.341
|
6.27e-07
|
1.158
|
| HMC_vs_SMC |
3
|
5.569
|
5.23e-06
|
1.017
|
| HMC_vs_SMC |
4
|
35.680
|
1.64e-25
|
6.514
|
| HMC_vs_SMC |
5
|
76.708
|
4.8e-35
|
14.005
|
| Metro_vs_SMC |
0
|
-1.624
|
0.115
|
-0.296
|
| Metro_vs_SMC |
1
|
-0.803
|
0.428
|
-0.147
|
| Metro_vs_SMC |
2
|
4.308
|
0.000173
|
0.786
|
| Metro_vs_SMC |
3
|
5.176
|
1.56e-05
|
0.945
|
| Metro_vs_SMC |
4
|
15.863
|
7.87e-16
|
2.896
|
| Metro_vs_SMC |
5
|
78.517
|
2.45e-35
|
14.335
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
1.016 |
0.179 |
0.075 |
11.177 |
| HMC |
2.5 |
0.802 |
0.180 |
0.073 |
8.505 |
| HMC |
3.0 |
1.441 |
0.123 |
0.047 |
28.030 |
| HMC |
4.0 |
1.864 |
0.127 |
0.051 |
34.282 |
| HMC |
10.0 |
5.036 |
0.101 |
0.049 |
99.713 |
| HMC |
50.0 |
5.115 |
0.126 |
0.063 |
79.582 |
| SMC |
2.1 |
0.737 |
0.179 |
0.075 |
7.442 |
| SMC |
2.5 |
0.503 |
0.180 |
0.073 |
4.421 |
| SMC |
3.0 |
0.212 |
0.123 |
0.047 |
1.892 |
| SMC |
4.0 |
0.157 |
0.127 |
0.051 |
0.596 |
| SMC |
10.0 |
0.101 |
0.101 |
0.049 |
0.008 |
| SMC |
50.0 |
0.101 |
0.126 |
0.063 |
-0.398 |
| Metro |
2.1 |
0.546 |
0.179 |
0.075 |
4.898 |
| Metro |
2.5 |
0.432 |
0.180 |
0.073 |
3.447 |
| Metro |
3.0 |
0.675 |
0.123 |
0.047 |
11.727 |
| Metro |
4.0 |
1.693 |
0.127 |
0.051 |
30.916 |
| Metro |
10.0 |
4.513 |
0.101 |
0.049 |
89.147 |
| Metro |
50.0 |
5.095 |
0.126 |
0.063 |
79.260 |
| DEMetro_Z |
2.1 |
1.082 |
0.179 |
0.075 |
12.051 |
| DEMetro_Z |
2.5 |
1.284 |
0.180 |
0.073 |
15.094 |
| DEMetro_Z |
3.0 |
1.407 |
0.123 |
0.047 |
27.289 |
| DEMetro_Z |
4.0 |
2.673 |
0.127 |
0.051 |
50.254 |
| DEMetro_Z |
10.0 |
3.525 |
0.101 |
0.049 |
69.183 |
| DEMetro_Z |
50.0 |
4.228 |
0.126 |
0.063 |
65.426 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
6.698 |
2.25e-07 |
15.937 |
| HMC |
2.5 |
5.800 |
2.54e-06 |
9.859 |
| HMC |
3.0 |
6.414 |
5.07e-07 |
28.675 |
| HMC |
4.0 |
5.970 |
1.72e-06 |
34.942 |
| HMC |
10.0 |
42.393 |
7.14e-28 |
102.742 |
| HMC |
50.0 |
157.757 |
4.12e-53 |
85.444 |
| SMC |
2.1 |
5.493 |
6.07e-06 |
10.184 |
| SMC |
2.5 |
3.431 |
0.00176 |
4.359 |
| SMC |
3.0 |
3.160 |
0.00306 |
1.514 |
| SMC |
4.0 |
1.748 |
0.086 |
0.499 |
| SMC |
10.0 |
-0.040 |
0.968 |
-0.011 |
| SMC |
50.0 |
-1.659 |
0.103 |
-0.389 |
| Metro |
2.1 |
2.992 |
0.00555 |
6.163 |
| Metro |
2.5 |
5.799 |
1.28e-06 |
3.185 |
| Metro |
3.0 |
4.545 |
8.75e-05 |
10.635 |
| Metro |
4.0 |
5.451 |
7.21e-06 |
30.249 |
| Metro |
10.0 |
16.436 |
2.97e-16 |
94.154 |
| Metro |
50.0 |
149.271 |
2.78e-51 |
85.312 |
| DEMetro_Z |
2.1 |
4.567 |
8.34e-05 |
16.691 |
| DEMetro_Z |
2.5 |
4.659 |
6.47e-05 |
17.391 |
| DEMetro_Z |
3.0 |
4.205 |
0.000228 |
26.726 |
| DEMetro_Z |
4.0 |
6.767 |
1.97e-07 |
49.829 |
| DEMetro_Z |
10.0 |
9.129 |
4.96e-10 |
73.725 |
| DEMetro_Z |
50.0 |
13.411 |
5.59e-14 |
71.480 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
1.413
|
0.168
|
0.258
|
| DEMetro_Z_vs_SMC |
1
|
3.272
|
0.00276
|
0.597
|
| DEMetro_Z_vs_SMC |
2
|
3.942
|
0.000468
|
0.720
|
| DEMetro_Z_vs_SMC |
3
|
6.709
|
2.33e-07
|
1.225
|
| DEMetro_Z_vs_SMC |
4
|
9.151
|
4.74e-10
|
1.671
|
| DEMetro_Z_vs_SMC |
5
|
13.477
|
5.14e-14
|
2.461
|
| HMC_vs_Metro |
0
|
2.922
|
0.00667
|
0.534
|
| HMC_vs_Metro |
1
|
3.879
|
0.000556
|
0.708
|
| HMC_vs_Metro |
2
|
4.069
|
0.000332
|
0.743
|
| HMC_vs_Metro |
3
|
0.652
|
0.52
|
0.119
|
| HMC_vs_Metro |
4
|
1.325
|
0.195
|
0.242
|
| HMC_vs_Metro |
5
|
0.218
|
0.829
|
0.040
|
| Metro_vs_DEMetro_Z |
0
|
-2.488
|
0.0189
|
-0.454
|
| Metro_vs_DEMetro_Z |
1
|
-3.811
|
0.000666
|
-0.696
|
| Metro_vs_DEMetro_Z |
2
|
-2.402
|
0.023
|
-0.438
|
| Metro_vs_DEMetro_Z |
3
|
-2.346
|
0.026
|
-0.428
|
| Metro_vs_DEMetro_Z |
4
|
1.892
|
0.0686
|
0.345
|
| Metro_vs_DEMetro_Z |
5
|
2.643
|
0.0131
|
0.483
|
| HMC_vs_SMC |
0
|
2.100
|
0.0446
|
0.383
|
| HMC_vs_SMC |
1
|
2.512
|
0.0178
|
0.459
|
| HMC_vs_SMC |
2
|
6.052
|
1.38e-06
|
1.105
|
| HMC_vs_SMC |
3
|
5.797
|
2.78e-06
|
1.058
|
| HMC_vs_SMC |
4
|
42.143
|
1.43e-27
|
7.694
|
| HMC_vs_SMC |
5
|
154.836
|
7.21e-44
|
28.269
|
| Metro_vs_SMC |
0
|
-1.599
|
0.121
|
-0.292
|
| Metro_vs_SMC |
1
|
-0.867
|
0.393
|
-0.158
|
| Metro_vs_SMC |
2
|
3.886
|
0.000545
|
0.709
|
| Metro_vs_SMC |
3
|
5.300
|
1.1e-05
|
0.968
|
| Metro_vs_SMC |
4
|
16.332
|
3.67e-16
|
2.982
|
| Metro_vs_SMC |
5
|
145.446
|
4.42e-43
|
26.555
|
| HMC_vs_DEMetro_Z |
0
|
-0.171
|
0.865
|
-0.031
|
| HMC_vs_DEMetro_Z |
1
|
-1.640
|
0.112
|
-0.299
|
| HMC_vs_DEMetro_Z |
2
|
0.250
|
0.805
|
0.046
|
| HMC_vs_DEMetro_Z |
3
|
-1.772
|
0.0869
|
-0.323
|
| HMC_vs_DEMetro_Z |
4
|
3.822
|
0.000647
|
0.698
|
| HMC_vs_DEMetro_Z |
5
|
2.586
|
0.015
|
0.472
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.105 |
0.010 |
0.006 |
15.937 |
| HMC |
2.5 |
0.089 |
0.014 |
0.008 |
9.859 |
| HMC |
3.0 |
0.175 |
0.010 |
0.006 |
28.675 |
| HMC |
4.0 |
0.234 |
0.012 |
0.006 |
34.942 |
| HMC |
10.0 |
0.603 |
0.010 |
0.006 |
102.742 |
| HMC |
50.0 |
0.619 |
0.013 |
0.007 |
85.444 |
| SMC |
2.1 |
0.071 |
0.010 |
0.006 |
10.184 |
| SMC |
2.5 |
0.047 |
0.014 |
0.008 |
4.359 |
| SMC |
3.0 |
0.019 |
0.010 |
0.006 |
1.514 |
| SMC |
4.0 |
0.015 |
0.012 |
0.006 |
0.499 |
| SMC |
10.0 |
0.010 |
0.010 |
0.006 |
-0.011 |
| SMC |
50.0 |
0.010 |
0.013 |
0.007 |
-0.389 |
| Metro |
2.1 |
0.047 |
0.010 |
0.006 |
6.163 |
| Metro |
2.5 |
0.038 |
0.014 |
0.008 |
3.185 |
| Metro |
3.0 |
0.071 |
0.010 |
0.006 |
10.635 |
| Metro |
4.0 |
0.204 |
0.012 |
0.006 |
30.249 |
| Metro |
10.0 |
0.554 |
0.010 |
0.006 |
94.154 |
| Metro |
50.0 |
0.618 |
0.013 |
0.007 |
85.312 |
| DEMetro_Z |
2.1 |
0.109 |
0.010 |
0.006 |
16.691 |
| DEMetro_Z |
2.5 |
0.146 |
0.014 |
0.008 |
17.391 |
| DEMetro_Z |
3.0 |
0.164 |
0.010 |
0.006 |
26.726 |
| DEMetro_Z |
4.0 |
0.329 |
0.012 |
0.006 |
49.829 |
| DEMetro_Z |
10.0 |
0.436 |
0.010 |
0.006 |
73.725 |
| DEMetro_Z |
50.0 |
0.520 |
0.013 |
0.007 |
71.480 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Forest & Ridge Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain